tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

rounding effects of quenched randomness on first order phase transitions frozen in disorder in an otherwise homogeneous system is modeled by interaction terms with random coefficients given by independent random variables with a translation invariant distribution for such systems it is proven that ind 2 dimensions there can be no first order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter discontinuities which would amount to a continuous symmetry breaking in systems which are stochastically invariant under the action of a continuous subgroup ofo n are suppressed by the randomness in dimensionsd 4 specific implications are found in the random field ising model for which we conclude that ind 2 dimensions at all h the gibbs state is unique for almost all field configurations and in the random bond potts model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point the results are explained by the argument of imry and ma 1 the proofs involve the analysis of fluctuations of free energy differences which are shown using martingale techniques to be gaussian on the suitable scale

maximum entropy principles for disordered spins we transform nonstationary independent random fields with exponential radon nikodym factors and study the asymptotics of the transformed processes as applications we deduce conditional limit theorems for such random fields and we study a curie weiss type mean field model of a quenched mixed magnetic crystal this model has quenched site disorder and frustration but non random coupling constants we find a continuous phase transition with critical exponents equal to those of the classical curie weiss theory

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

buchsbaum rim sheaves and their multiple sections abstract this paper begins by introducing and characterizing buchsbaum rim sheaves on z proj r where r is a graded gorenstein k algebra they are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free r modules then we study multiple sections of a buchsbaum rim sheaf b i e we consider morphisms p b of sheaves on z dropping rank in the expected codimension where h0 z p is a free r module the main purpose of this paper is to study properties of schemes associated to the degeneracy locus s of it turns out that s is often not equidimensional let x denote the top dimensional part of s in this paper we measure the difference between x and s compute their cohomology modules and describe ring theoretic properties of their coordinate rings moreover we produce graded free resolutions of x and s which are in general minimal among the applications we show how one can embed a subscheme into an arithmetically gorenstein subscheme of the same dimension and prove that zero loci of sections of the dual of a null correlation bundle are arithmetically buchsbaum

multidimensional random subshifts of finite type and their large deviations i introduce random multidimensional subshifts of finite type which generalize models of spin glasses and establish the almost sure large deviations bounds for gibbs measures there the paper is sequel to ekw where the corresponding results were obtained for deterministic multidimensional subshifts of finite type

relative entropy and variational properties of generalized gibbsian measures we study the relative entropy density for generalized gibbs measures we first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of almost gibbsian measures almost sure continuity of conditional probabilities for quasilocal measures we obtain a full variational principle for the joint measures of the random field ising model we show that the weak gibbs property holds with an almost surely rapidly decaying translation invariant potential for these measures we show that the variational principle fails as soon as the measures lose the almost gibbs property these examples suggest that the class of weakly gibbsian measures is too broad from the perspective of a reasonable thermodynamic formalism

entropy for translation invariant random cluster measures we study translation invariant random cluster measures with techniques from large deviation theory and convex analysis in particular we prove a large deviation principle with rate function given by a specific entropy and a dobrushinlanfordruelle variational principle that characterizes translation invariant random cluster measures as the solutions of the variational equation for free energy consequences of these theorems include inequalities for edge and cluster densities of translationinvariant random cluster measures 1 introduction the random cluster model was introduced around 1972 by fortuin and kasteleyn 18 as a family of models that contains the bernoulli bond percolation model the ising model and the q state potts models as special cases it has developed into an important and very successful tool for studying the ising and potts models our paper focuses on the properties of the random cluster measures themselves our starting point is grimmett s 23 development of elements of a thermodynamic formalism for this model beginning with a definition of infinite volume random cluster measures in terms of a dlr dobrushinlanfordruelle equation just as for gibbsian systems natural next questions concern the validity of large deviation principles and variational characterizations of infinite volume measures these questions we answer in the present paper and derive some consequences here is a brief overview of the dlr approach of 23 the random cluster measures of interest live on the graph formed by putting edges between nearest neighbor vertices of the d dimensional hypercubic lattice d the edge that connects two vertices x and y that are l 1 distance one apart is

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

the general hyperplane section of a curve in this paper we discuss some necessary and sufficient conditions for a curve to be arithmetically cohen macaulay in terms of its general hyperplane section we obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically cohen macaulay curve of p 3 we prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non arithmetically cohen macaulay curve of p 3 arise also as degree matrices of some smooth integral non arithmetically cohen macaulay curve and we characterize the exceptions we give a necessary condition on the graded betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve in p for curves in p 3 we show that any set of betti numbers that satisfies that condition can be realized as the betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve we also show that the matrices that arise as a degree matrix of the general plane section of an arithmetically buchsbaum integral smooth non arithmetically cohen macaulay space curve are exactly those that arise as a degree matrix of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay space curve and have positive subdiagonal we also prove some bounds on the dimension of the deficiency module of an arithmetically buchsbaum space curve in terms of the degree matrix of the general plane section of the curve and we prove that they are sharp

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

on direct convergence and periodicity for transition probabilities of markov chains in random environments we study direct convergence of the products p theta 0 cdots p theta n of random stochastic matrices these products can be interpreted as the transition probabilities of nonhomogeneous markov chains selected at random by a stationary environmental sequence theta n in other words a markov chain in a random environment rather than make assumptions analogous to irreducibility and aperiodicity for homogeneous markov chains we introduce equivalence relations that allow convergence results on the equivalence classes the classical decomposition into a cycle of periodic sets is not possible in general so the periodicity in the title is meant only to be suggestive we also examine the frequency of times of positive probability of return to a state or set

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

hilbert function of powers of ideals of low codimension we study the hilbert function of the powers of homogeneous ideals which are either cohen macaulay of codimension 2 or gorenstein of codimension 3 we show that that if i is an ideal in one of these classes and it is of linear type then for all k the hilbert function of i k depends only on the hilbert function of i in other words if i andj are ideals in one of the above mentioned classes which are both of linear type and they have the same hilbert function then also i k and j k have the same hilbert function for all k

non degenerate curves with maximal hartshorne rao module extending results for space curves we establish bounds for the cohomology of a non degenerate curve in projective n space as a consequence for any given n we determine all possible pairs d g where d is the degree and g is the arithmetic genus of the curve furthermore we show that curves attaining our bounds always exist and describe properties of these extremal curves in particular we determine the hartshorne rao module the generic initial ideal and the graded betti numbers of an extremal curve

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

weakly gibbsian representations for joint measures of quenched lattice spin models can the joint measures of quenched disordered lattice spin models with finite range on the product of spin space and disorder space be represented as suitably generalized gibbs measures of an annealed system we prove that there is always a potential depending on both spin and disorder variables that converges absolutely on a set of full measure w r t the joint measure weak gibbsianness this positive result is surprising when contrasted with the results of a previous paper k6 where we investigated the measure of the set of discontinuity points of the conditional expectations investigation of a s gibbsianness in particular we gave natural negative examples where this set is even of measure one including the random field ising model further we discuss conditions giving the convergence of vacuum potentials and conditions for the decay of the joint potential in terms of the decay of the disorder average over certain quenched correlations we apply them to various examples from this one typically expects the existence of a potential that decays superpolynomially outside a set of measure zero our proof uses a martingale argument that allows to cut an infinite volume analogue of the quenched free energy into local pieces along with generalizations of kozlov s constructions

crossed products by endomorphisms and reduction of relations in relative cuntz pimsner algebras abstract starting from an arbitrary endomorphism of a unital c algebra a we construct a crossed product it is shown that the natural construction depends not only on the c dynamical system a but also on the choice of an ideal j orthogonal to ker the article gives an explicit description of the internal structure of this crossed product and in particular discusses the interrelation between relative cuntz pimsner algebras and partial isometric crossed products we present a canonical procedure that reduces any given c correspondence to the smallest c correspondence yielding the same relative cuntz pimsner algebra as the initial one in the context of crossed products this reduction procedure corresponds to the reduction of c dynamical systems and allows us to establish a coincidence between relative cuntz pimsner algebras and crossed products introduced

metastates in disordered mean field models ii the superstates we continue to investigate the size dependence of disordered mean field models with finite local spin space in more detail illustrating the concept of superstates as recently proposed by bovier and gayrard we discuss various notions of convergence for the behavior of the paths t tn t 0 1 in the thermodynamic limit n here n is the gibbs measure in the finite volume 1 n and is the disorder variable in particular we prove refined convergence statements in our concrete examples the hopfield model with finitely many patterns having continuous paths and the curie weiss random field ising model having singular paths

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

deformations of modules of maximal grade and the hilbert scheme at determinantal schemes let r be a polynomial ring and m a finitely generated graded r module of maximal grade which means that the ideal it a generated by the maximal minors of a homogeneous presentation matrix a of m has maximal codimension in r suppose x proj r it a is smooth in a sufficiently large open subset and dimx 1 then we prove that the local graded deformation functor of m is isomorphic to the local hilbert scheme functor at x proj r under a weak assumption which holds if dimx 2 under this assumption we get that the hilbert scheme is smooth at x and we give an explicit formula for the dimension of its local ring as a corollary we prove a conjecture of r m miro roig and the author that the closure of the locus of standard determinantal schemes with fixed degrees of the entries in a presentation matrix is a generically smooth component v of the hilbert scheme also their conjecture on the dimension of v is proved for dimx 1 the cohomology h i nx of the normal sheaf of x in proj r is shown to vanish for 1 i dimx 2 finally the mentioned results slightly adapted remain true replacing r by any cohen macaulay quotient of a polynomial ring

dimension of families of determinantal schemes a scheme x p n c of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the maximal minors of a homogeneous t x t c 1 matrix and x is said to be good determinantal if it is standard determinantal and a generic complete intersection given integers a 0 a 1 a t c 2 and b 1 b t we denote by w b a c hilb p p n c resp w s b a the locus of good resp standard determinantal schemes x c p n c of codimension c defined by the maximal minors of a t x t c 1 matrix f ij i 1 t j 0 t c 2 where f ij k x 0 x 1 x n c is a homogeneous polynomial of degree a j b i in this paper we address the following three fundamental problems to determine 1 the dimension of w b a resp w s b a in terms of a j and b i 2 whether the closure of w b a is an irreducible component of hilb p p n c and 3 when hilb p p n c is generically smooth along w b a concerning question 1 we give an upper bound for the dimension of w b a resp w s b a which works for all integers a 0 a 1 a t c 2 and b 1 b t and we conjecture that this bound is sharp the conjecture is proved for 2 2 and for c 5 under certain numerical assumptions

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

an iterative construction of gorenstein ideals in this paper we present a method to inductively construct gorenstein ideals of any codimension c we start from a gorenstein ideal i of codimension c contained in a complete intersection ideal j of the same codimension and we prove that under suitable hypotheses there exists a new gorenstein ideal contained in the residual ideal i j we compare some numerical data of the starting and the resulting gorenstein ideals of the construction we compare also the buchsbaum eisenbud matrices of the two ideals in the codimension three case furthermore we show that this construction is independent from the other known geometrical constructions of gorenstein ideals providing examples

purely infinite crossed products by endomorphisms 2013 elsevier inc all rights reserved this is the authors accepted and refereed manuscript to the article author s post print must be released with a creative commons attribution non commercial no derivatives license

pure infiniteness and ideal structure of c algebras associated to fell bundles abstract we investigate structural properties of the reduced cross sectional algebra c r b of a fell bundle b over a discrete group g conditions allowing one to determine the ideal structure of c r b are studied notions of aperiodicity paradoxicality and b infiniteness for the fell bundle b are introduced and investigated by themselves and in relation to the partial dynamical system dual to b several criteria of pure infiniteness of c r b are given it is shown that they generalize and unify corresponding results obtained in the context of crossed products by the following duos laca spielberg 34 jolissaint robertson 21 sierakowski rordam 47 giordano sierakowski 18 and ortega pardo 39 for exact separable fell bundles satisfying the residual intersection property primitive ideal space of c r b is determined the results of the paper are shown to be optimal when applied to graph c algebras applications to a class of exel larsen crossed products are presented

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

simple purely infinite c algebras and n filling actions let n be a positive integer we introduce a concept which we call the n filling property for an action of a group on a separable unital c algebra a if a c is a commutative unital c algebra and the action is induced by a group of homeomorphisms of then the n filling property reduces to a weak version of hyperbolicity the n filling property is used to prove that certain crossed product c algebras are purely infinite and simple a variety of group actions on boundaries of symmetric spaces and buildings have the n filling property an explicit example is the action of sln z on the projective n space

phase transition in the 3d random field ising model we show that the three dimensional ising model coupled to a small random magnetic field is ordered at low temperatures this means that the lower critical dimension dl for the theory isdl 2 settling a long controversy on the subject our proof is based on an exact renormalization group rg analysis of the system this analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of imry and ma the rg acts in the space of ising models and in the space of random field distributions driving the former to zero temperature and the latter to zero variance

metastates in disordered mean field models random field and hopfield models we rigorously investigate the size dependence of disordered mean field models with finite local spin space in terms of metastates thereby we provide an illustration of the framework of metastates for systems of randomly competing gibbs measures in particular we consider the thermodynamic limit of the empirical metastate 1 n sum nolimits n 1 n delta mu eta eta where n is the gibbs measure in the finite volume 1 n and the frozen disorder variable is fixed we treat explicitly the hopfield model with finitely many patterns and the curie weiss random field ising model in both examples in the phase transition regime the empirical metastate is dispersed for largen moreover it does not converge for a e but rather in distribution for whose limits we given explicit expressions we also discuss another notion of metastates due to aizenman and wehr

correction added in proof we extend sanov s theorem on i i d large deviations to independent but not identically distributed random variables and study the generalization of relative entropy that appears as the rate function

liaison equivalence classes we will work in ip n 2 over an algebraically closed field the notion of liaison among subvarieties of ip was introduced in 3 we will consider here liaison in codimension two generalizing results in 4 recall therefore that two subschemes v 1 v 2 of ip that are locally cohenmacaulay and equidimensional of codimension two are said to be linked algebraically via the complete intersection x of two hypersurfaces denoted v l v z via x if d e v j x v r o v x t j they are said to be linked geometrically if i 1 and v2 in the above definition have no components in common according to 4 theorem 1 7 the two notions of linkage generate the same equivalence relation among those subschemes v which are also generically locally complete intersections we will hence consider only algebraic linkage

linkage and the koszul homology of ideals 0 introduction let r be a local ring and i an ideal of r associated to i are several graded algebras the symmetric algebra of the module i sym i the rees algebra of i defined to be the algebra r i gn o inf and the associated graded algebra of i gr1 r rii g ii 2 in in 1 i i i our purpose in this paper is to study the behavior of these graded algebras when we change i through linkage recall the definition of linkage found in the paper of peskine and szpiro 22

maximal families of gorenstein algebras the purpose of this paper is to study maximal irreducible families of gorenstein quotients of a polynomial ring r let gradalg h r be the scheme parametrizing graded quotients of r with hilbert function h we prove there is a close relationship between the irreducible components of gradalg h r whose general member is a gorenstein codimension c 1 quotient and the irreducible components of gradalg h r whose general member b is a codimension c cohen macaulay algebra of hilbert function h related to h if the castelnuovo mumford regularity of the gorenstein quotient is large compared to the castelnuovo mumford regularity of b this relationship actually determines a well defined injective mapping from such cohen macaulay components of gradalg h r to gorenstein components of gradalg h r in which generically smooth components correspond moreover the dimension of the gorenstein components is computed in terms of the dimension of the corresponding cohen macaulay component and a sum of two invariants of b using linkage by a complete intersection we show how to compute these invariants linkage also turns out to be quite effective in verifying the assumptions which appear in a generalization of the main theorem

large deviations and maximum entropy principle for interacting random fields on mathbb z d we present a new approach to the principle of large deviations for the empirical field of a gibbsian random field on the integer lattice zd this approach has two main features first we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities and thus obtain estimates which are finer and more widely applicable second we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field the limits being those predicted by the maximum entropy principle this result implies a general version of the equivalence of gibbs ensembles stating that every microcanonical limiting state is a grand canonical equilibrium state we also prove a converse to the last statement and discuss some applications 0 introduction as is well known the study of the asymptotic probabilities of large fluctuations of time averages or space averages away from the mean is based on two fundamental principles the principle of large deviations and the maximum entropy principle the former provides the exact rate of exponential decay of the fluctuation probabilities whereas the latter predicts the limiting conditional distribution under the condition that the fluctuations are large it is obvious that these principles are intimately related in this paper we investigate these principles in the case of interacting random fields on the integer lattice 7zd the setup is the following first we let e 4 be any measurable space we shall assume throughout that e a is standard borel but we shall avoid making any explicit topological assumptions on e so we do not assume that e is polish next we let s zd be the d dimensional integer lattice and q f e gas the associated product space in lattice models of statistical mechanics e is called the state space or single spin space and q f the configuration space we let j s f denote the set of all probability

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

on the normal sheaf of determinantal varieties o roig abstract let x be a standard determinantal scheme xp n of codimension c i e a scheme defined by the maximal minors of a t t c 1 homogeneous polynomial matrix a in this paper we study the main features of its normal sheaf nx we prove that under some mild restrictions 1 there exists a line bundle l on x sing x such that nx l is arithmetically cohen macaulay and even more it is ulrich whenever the entries of a are linear forms 2 nx is simple hence indecomposable and finally 3 nx is semi stable provided the entries of a are linear forms

order ideals and a generalized krull height theorem let n be a finitely generated module over a noetherian local ring r m we give criteria for the height of the order ideal n x of an element x n to be bounded by the rank of n the generalized principal ideal theorem of bruns eisenbud and evans says that this inequality always holds if x mn we show that the inequality even holds if the hypothesis becomes true after first extending scalars to some local domain and then factoring out torsion we give other conditions in terms of residual intersections and integral closures of modules we derive information about order ideals that leads to bounds on the heights of trace ideals of modules even in circumstances where we do not have the expected bounds for the heights of the order ideals

a c algebra of singular integral operators with shifts admitting distinct fixed points abstract representations on hilbert spaces for a nonlocal c algebra b of singular integral operators with piecewise slowly oscillating coefficients extended by a group of unitary shift operators are constructed the group of unitary shift operators u g in the c algebra b is associated with a discrete amenable group g of orientation preserving piecewise smooth homeomorphisms g t t that acts topologically freely on t and admits distinct fixed points for different shifts a c algebra isomorphism of the quotient c algebra b k where k is the ideal of compact operators onto a c algebra of fredholm symbols is constructed by applying the local trajectory method spectral measures and a lifting theorem as a result a fredholm symbol calculus for the c algebra b or equivalently a faithful representation of the quotient c algebra b k on a suitable hilbert space is constructed and a fredholm criterion for the operators b b is established

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

large deviations for lattice systems i parametrized independent fields we prove large deviation theorems for empirical measures of independent random fields whose distributions depend measurably on an auxiliary parameter this dependence respects the action of the shift group and a large deviation principle holds whenever a certain ergodicity condition is satisfied we also investigate the entropy functions for these processes especially in relation to the usual relative entropy

large deviation principles for euclidean functionals and other nearly additive processes we prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or euclidean space under approximate additivity and regularity hypotheses the rate function is the convex dual of the limiting logarithmic moment generating function in some applications the rate function can be expressed in terms of relative entropy the general result applies to processes in euclidean combinatorial optimization statistical mechanics and computational geometry examples include the length of the minimal tour the traveling salesman problem the length of the minimal matching graph the length of the minimal spanning tree the length of the k nearest neighbors graph and the free energy of a short range spin glass model

the ergodic theory of markov chains in random environments a general formulation of the stochastic model for a markov chain in a random environment is given including an analysis of the dependence relations between the environmental process and the controlled markov chain in particular the problem of feedback assuming stationary environments the ergodic theory of markov processes is applied to give conditions for the existence of finite invariant measure equilibrium distributions and to obtain ergodic theorems which provide results on convergence of products of random stochastic matrices coupling theory is used to obtain results on direct convergence of these products and the structure of the tail field state properties including classification and communication properties are discussed

quenched large deviations for interacting diffusions in random media the aim of the paper is to establish a large deviation principle ldp for the empirical measure of mean field interacting diffusions in a random environment the point is to derive such a result once the environment has been frozen quenched model the main theorem states that a ldp holds for every sequence of environment satisfying appropriate convergence condition with a rate function that does not depend on the disorder and is different from the rate function in the averaged model similar results concerning the empirical flow and local empirical measures are provided

the structure of the inverse system of gorenstein k algebras abstract macaulay s inverse system gives an effective method to construct artinian gorenstein k algebras to date a general structure for gorenstein k algebras of any dimension and codimension is not understood in this paper we extend macaulay s correspondence characterizing the submodules of the divided power ring in one to one correspondence with gorenstein d dimensional k algebras we discuss effective methods for constructing gorenstein graded rings several examples illustrating our results are given

sheaves with canonical determinant on cohen macaulay schemes abstract this paper studies the class of sheaves which lie on arithmetically cohen macaulay schemes and which have as determinant a twist of the canonical sheaf special emphasis is placed on finding minimal sufficient cohomological conditions which ensure that the top dimensional component of regular sections of the dual of these sheaves vanish along arithmetically gorenstein schemes duals of odd rank buchsbaum rim sheaves normal sheaves to licci schemes certain sheafified koszul homology modules and various other families are shown to satisfy the requisite conditions

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

crossed products by spectrally free actions abstract we define spectral freeness for actions of discrete groups on c algebras we relate spectral freeness to other freeness conditions an example result is that for an action of a finite group g spectral freeness is equivalent to strong pointwise outerness and also to the condition that g 1 for every g g 1 we then prove permanence results for reduced crossed products by exact spectrally free actions for crossed products by arbitrary actions of z 2 z and for extensions direct limits stable isomorphism and several related constructions for the following properties the combination of pure infiniteness and the ideal property residual hereditary infiniteness closely related to pure infiniteness residual sp a strengthening of property sp suitable for nonsimple c algebras the weak ideal property closely related to the ideal property for the weak ideal property we can allow arbitrary crossed products by any finite abelian group these properties of c algebras are shown to have formulations of the same general type allowing them all to be handled using a common set of theorems

numerical invariants of liaison classes 302 c huneke intersection what properties are then enjoyed by v for instance buchweitz was able to show that all such v are strongly nonobstructed see 5 for details the two questions above have been completely answered if x spec r with r a regular local ring and if codim v 2 in this case

topological freeness for c correspondences abstract we study conditions that ensure uniqueness theorems of cuntz krieger type for relative cuntz pimsner algebras o j x associated to a c correspondence x over a c algebra a we give general sufficient conditions phrased in terms of a multivalued map x acting on the spectrum a of a when x j is of type i we construct a directed graph dual to x and prove a uniqueness theorem using this graph when x j is liminal we show that topological freeness of this graph is equivalent to the uniqueness property for o j x as well as to an algebraic condition which we call j acyclicity of x as an application we improve the fowler raeburn uniqueness theorem for the toeplitz algebra t x we give new simplicity criteria for o x we generalize and enhance uniqueness results for relative quiver c algebras of muhly and tomforde we also discuss applications to crossed products by endomorphisms

the minimal free resolution of the migliore peterson rings in the case that the reflexive sheaf has even rank abstract letrbe a commutative noetherian ring and f gbe a homomorphism of freer modules where rank f fand rank g g fix an elementbg 1 g 1fand a generator g for gg the module action of f on fproduces the elementb1 g g bg 1 inf letjdenote the image ofb1 f r assume that gradej f g which is the largest grade possible and is attained in the generic case the idealjmay be interpreted as the defining ideal of the degeneracy locus of a regular section of a rankf greflexive sheaf it may also be interpreted as the order ideal of an element in a second syzygy module of rankf g also jmay be interpreted as the defining ideal for the symmetric algebra of a module of projective dimension two migliore and peterson have studied the idealjunm which is the unmixed part ofj under geometric hypotheses they have shown thatr junmis a cohen macaulay ring and they have resolved this ring furthermore iff gis odd thenjunmis a gorenstein ideal and is not equal toj on the other hand iff gis even thenjunm j in the present paper we produce the resolution ofr jby freer modules in the case thatf gis even and f g 2 is a unit inr our resolution is minimal whenever the data are local or homogeneous our resolution is built from the differential graded algebra f x1 xg d where the restriction ofdto f is the koszul complex associated tob1 f rand the degree two divided power variablesx1 xghave been adjointed in order to kill the cycles g 1f the acyclicity lemma is used to prove exactness ifg 1 then the idealjis equal to the huneke ulrich almost complete intersection ideali1 yx whereyis a 1 fmatrix andxis anf falternating matrix the resolution of this ideal is already known

statistics and meta statistics in the concept of complexity abstract a crucial distinction between different classes of complexity measures is found to consist in their statistical structure while first order statistics always provides one or another kind of a measure of randomness second order meta statistics provides more subtle measures of complexity an example of a second order measure is constructed and applied to specific cases some formal and conceptual issues concerning the general relevance of meta statistical concepts of complexity are pointed out

maximal cohen macaulay modules and gorenstein algebras abstract let b be a graded cohen macaulay quotient of a gorenstein ring r it is known that sections of the dual of the canonical module kb can be used to construct gorenstein quotients of r the purpose of this paper is to place this method of construction into a broader context if m is a maximal cohen macaulay b module whose sheafified top exterior power is a twist of kb and if m satisfies certain additional homological conditions then regular sections of m can again be used to construct gorenstein quotients of r on cohen macaulay quotients the normal module the first koszul homology module and several other associated modules all have sheafified top exterior power equal to a twist of kb if additional restrictions are placed on the cohen macaulay quotients then these modules will satisfy the required additional homological conditions this places the canonical module within a broad family of easily manipulated maximal cohen macaulay modules whose sections can be used to construct gorenstein quotients of r

large deviation estimates for a conditional probability distribution applications to random interaction gibbs measures let x i y i d be independent identically distributed random variables with arbitrary distribution we show that for almost every y i i the conditional law of the empirical field given y i i satisfies to large deviation inequalities this applies to the study of gibbs measures with random interaction in the case of some mean field models as well as of short range summable interaction we show that the pressure is nonrandom and is given by a variational formula these random gibbs measures have the same large deviation rate which does not depend on the particular realization of the interaction their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula