weak singularity and absence of metastability in random ising ferromagnets in the above models there exists a weak singularity of the magnetisation in addition to its jump on the first order transition line it corresponds to the griffiths 1969 singularity above the temperature of the phase transition analytic continuation from positive to negative magnetic fields yielding a metastable state is impossible

improved perturbation expansion for disordered systems beating griffiths singularities we introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge due to the presence of griffiths type singularities it is organized inductively over an infinite sequence of increasing distance scales in each induction step one redefines what is means by the unperturbed system a procedure somewhat reminiscent of k a m theory our techniques may be useful in dealing with the so called large field problem in real space renormalization group schemes

self similar singular solutions of a p laplacian evolution equation with absorption we consider for pa 1 2 and q 1 self similar singular solutions of the equation vt div jrvj p 2 rv v q in r n 0 n here by self similar we mean that v takes the form

renormalization group in the uniqueness region weak gibbsianity and convergence we analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature we prove weak gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system the correlation length or the critical length for metastability or both thus to perturbatively treat the problem we have to use a scale adapted expansion moreover such a model below the critical temperature resembles a disordered system in the presence of griffiths singularity then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached

complete classification of shape functions of self similar solutions abstract in this paper we study some asymptotic profiles of shape functions of self similar solutions to the initial boundary value problem with neumann boundary condition for the generalized kpz equation u t u x x u x q where q is positive number the shapes of solutions of the corresponding nonlinear ordinary differential equation are of very different nature the properties depend on the critical value q 1 3 2 2 and initial data as usual

existence and non existence results for ground states of quasilinear elliptic equations we consider the quasilinear equation introduced by chipot weissler delta u u p nabla u q 0 in r n i in rn where p and q are given positive exponents and n 3 of particular interest is the question of existence and non existence of radial ground states that is non negative non trivial radial solutions defined for all r 0 using shooting methods general poincare inequalities and poho aev pucci serrin type iden tities we establish existence if either i p l ii p l q p iii p l i p l ii p l q p iii p l q frac 2p p 1 where l is the critical value n 2 n 2 on the other hand putting l1 n n 2 we show that if either i q underset raise0 3em hbox smash scriptscriptstyle geqslant frac 2p p 1 0 frac 2p p 1 1 underset raise0 3em hbox smash scriptscriptstyle leqslant p underset raise0 3em hbox smash scriptscriptstyle leqslant l 1 iii q underset raise0 3em hbox smash scriptscriptstyle geqslant bar q l 1 p underset raise0 3em hbox smash scriptscriptstyle leqslant l then radial ground states for i cannot exist where q is a function of p and n such that 2p p 1 q p for l1 p l and q p for p l

global solutions of the fast diffusion equation with gradient absorption terms abstract we investigate the existence of nonnegative weak solutions to the problem u t u m u p in r n 0 with 1 2 n m 1 it will be proved that i when 1 p 2 if the initial datum u 0 d r n then there exists a solution ii when 1 p 2 m n n 1 if the initial datum u 0 x is a bounded and nonnegative measure then the solution exists iii when 2 m n n 1 p 2 if the initial datum is a dirac mass then the solution does not exist we also study the large time behavior of the l 1 norm of solutions for 1 p 2 m n n 1 and the large time behavior of t 1 u t e c t l for 2 m n n 1 p 2

almost gibbsian description of the sign fields of sos fields an example is presented of a measure on a lattice system which has a measure zero set of points configurations where some conditional probability can be discontinuous but does not become a gibbs measure under decimation or other transformations we also discuss some related issues

decay of two point functions for d 1 dimensional percolation ising and potts models with d dimensional disorder let left j left langle x y right rangle right left langle x y right rangle subset z d and left k x right x in z d be independent sets of nonnegative i i d r v s denoting a pair of nearest neighbors inzd let 0 we consider the random systems 1 a bond bernoulli percolation model onzd 1 with random occupation probabilities open image in new window 2 ferromagnetic random ising potts models onzd 1 in the ising case the hamiltonian is h beta sum limits t sum limits left langle x y right rangle j left langle x y right rangle sigma x t sigma y t gamma sum limits x sum limits t k x sigma x t sigma x t 1 for such d 1 dimensional systems withd dimensional disorder we prove i for anyd 1 if and are small then with probability one the two point functions decay exponentially in thed dimensional distance and faster than polynomially in the remaining dimension ii ifd 2 then with probability one we have long range order for either and with sufficiently large of sufficiently large and any

a very singular solution of a quasilinear degenerate diffusion equation with absorption the object of this paper is to study the existence of a nonnegative solution of the cauchy problem ut div vu p 2vu u u x 0 0 if i 0 which is more singular at 0 0 than the fundamental solution of the corre sponding equation without the absorption term when 1 1 by this was meant a solution w x t with the properties i w 0 in s ii w is smooth in s except at 0 0 iii w x 0 0 for all x e rn except at x 0 iv w is more singular at the origin than the fundamental solution e of the heat equation specifically

a very singular solution of the porous media equation with absorption turns out to play an important role in the description of both the short and the long time behaviour of positive solutions of eq 1 1 for the short time behaviour it provides together with the one parameter family of singular solutions i of problem i a complete description of the possible types of singular behaviour at the point 0 o 121 for the long time behaviour of solutions u x t of the cauchy problem for 1 1 1 2 it provides the asymptotic form when the initial function decays sufficiently fast as 1x1 co t p u x t w x t 0 ast co uniformly in r 7 81 in this paper we shall show that if

expansions in statistical physics on presente un traitement auto contenu du developpement polymere on axiomatise cette notion on demontre comment ces developpements permettent un traitement systematique de la plupart des developpements en amas de la physique statistique

phase diagrams and cluster expansions for low temperature models i the phase diagram low temperature phase diagrams of two dimensional open image in new window quantum field models are constructed let open image in new window lie in an r 1 dimensional space of perturbations of a polynomial withr degenerate minima perform a scaling open image in new window and assume 1 we constructk distinct states on left begin array 20 c r k end array right hypersurfaces of codimensionk 1 in the space of perturbations an expansion is used to exhibit exponential clustering of the schwinger functions of each of these states at the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima we draw on ideas of pirogov and sinai 24 for this problem

perturbative analysis of disordered ising models close to criticality we consider a two dimensional ising model with random i i d nearest neighbor ferromagnetic couplings and no external magnetic field we show that if the probability of supercritical couplings is small enough the system admits a convergent cluster expansion with probability one the associated polymers are defined on a sequence of increasing scales in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity the basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

very singular solutions to a nonlinear parabolic equation with absorption ii uniqueness we prove the uniqueness of the very singular solution to a hamilton jacobi equation with absorption we mention thatthe very singular solutions play an important role in the description of the large time behavior of the solutions

l estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms abstract we study the nonnegative solutions of the viscous hamilton jacobi problem u t u u q 0 u 0 u 0 in q t 0 t where q 1 0 t 0 and r n or is a smooth bounded domain and u 0 l r r 1 or u 0 m b we show l decay estimates valid for any weak solution without any conditions as x and without uniqueness assumptions as a consequence we obtain new uniqueness results when u 0 m b and q n 2 n 1 or u 0 l r and q n 2 r n r we also extend some decay properties to quasilinear equations of the model type u t p u u 1 u u q 0 where p 1 0 and u is a signed solution

feature extraction for texture discrimination via random field models with random spatial interaction in this paper we attack the problem of distinguishing textured images of real surfaces using small samples we first analyze experimental data that results from applying ordinary conditional markov fields in the face of the disappointing performance of these models we introduce a random field with spatial interaction that is itself a random variable usually referred to as a random field in a random environment for this class of models we establish the power spectrum and the autocorrelation function as well defined quantities and we devise a scheme for the estimation of related parameters the new set of features that resulted from this approach was applied to real images accurate discrimination was observed even for boxes of size 10 spl times 16

relaxation of disordered magnets in the griffiths regime we study the relaxation to equilibrium of discrete spin systems with random finite range not necessarily ferromagnetic interactions in the griffiths regime we prove that the speed of convergence to the unique reversible gibbs measure is almost surely faster than any stretched exponential at least if the probability distribution of the interaction decays faster than exponential e g gaussian furthermore if the interac tion is uniformly bounded the average over the disorder of the time autocorrelation function goes to equilibrium as exp k log t d d 1 in d 1 in agreement with previous results obtained for the dilute ising model

duality between invariant spaces for max plus linear discrete event systems we extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max plus or tropical semiring we establish a duality theorem relating both notions which we use to construct dynamic observers these are useful in situations in which some of the system coefficients may vary within certain intervals the results are illustrated by an application to a manufacturing system

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

graded cluster expansion for lattice systems in this paper we develop a general theory which provides a unified treatment of two apparently different problems the weak gibbs property of measures arising from the application of renormalization group maps and the mixing properties of disordered lattice systems in the griffiths phase we suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely large regions are widely separated we then show how it is possible to construct a convergent multi scale cluster expansion

max plus a b invariant spaces and control of timed discrete event systems the concept of a b invariant subspace or controlled invariant of a linear dynamical system is extended to linear systems over the max plus semiring although this extension presents several difficulties which are similar to those encountered in the same kind of extension to linear dynamical systems over rings it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings sufficient conditions are given for computing the maximal a b invariant subspace contained in a given space and the existence of linear state feedbacks is discussed an application to the study of transportation networks which evolve according to a timetable is considered

shrinking self similar solutions of a nonlinear diffusion equation with nondivergence form abstract in this paper we study the shrinking self similar solutions of the nonlinear diffusion equation with nondivergence form u t u m u m 1 this kind of solutions possess the properties of finite speed propagation of perturbations and their supports are shrinking we establish the existence and uniqueness for this kind of solutions in addition we study some properties of the shrinking self similar solutions

observer design for max linear systems this technical note deals with the state estimation for max plus linear systems this estimation is carried out following the ideas of the observer method for classical linear systems the system matrices are assumed to be known and the observation of the input and of the output is used to compute the estimated state the observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring

source type solutions of the porous media equation with absorption the fast diffusion case in this paper we consider the cauchy problem u t u m u p on s t r n 0 t u x 0 0 x r n 0 where n 1 p 1 and 0 m 1

a combinatorial proof of tree decay of semi invariants we consider finite range gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi invariants supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions this hypothesis holds for completely analytical gibbs fields in this context the tree decay of semi invariants has been proven via analyticity arguments however the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so called griffiths phase when analyticity arguments fail

two connections between random systems and non gibbsian measures in this contribution we discuss the role disordered or random systems have played in the study of non gibbsian measures this role has two main aspects the distinction between which has not always been fully clear 1 from disordered systems disordered systems can be used as a tool analogies with as well as results and methods from the study of random systems can be employed to investigate non gibbsian properties of a variety of measures of physical and mathematical interest 2 of disordered systems non gibbsianness is a property of various joint measures describing quenched disordered systems we discuss and review this distinction and a number of results related to these issues moreover we discuss the mean field version of the non gibbsian property and present some ideas how a kac limit approach might connect the finite range and the mean field non gibbsian properties

large time behavior for the fast diffusion equation with critical absorption we study the large time behavior of nonnegative solutions to the cauchy problem for a fast diffusion equation with critical zero order absorption partial t u delta u m u q 0 quad quad hbox in 0 infty times real n with m c n 2 n 1

the cauchy problem for ut δu u q with q a positive real number the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces in that context it is known as the generalized deterministic kpz equation the paper is concerned with the initial value problem for the equation under the assumption that the initial data function is bounded and continuous results on the existence uniqueness and regularity of solutions are obtained

strong decay to equilibrium in one dimensional random spin systems we consider a spin system on a lattice with finite range possibly unbounded random interactions we show that for such systems the glauber dynamics cannot decay to equilibrium exponentially fast inl2 even at high temperatures additionally for one dimensional systems with unbounded random couplings we prove that with probability one the corresponding glauber dynamics has a fast subexponential decay to equilibrium in the uniform norm provided that the distribution of random couplings satisfies some exponential bound

classification of singular solutions of a nonlinear heat equation on considere toutes les solutions non negatives de l equation de la chaleur non lineaire avec absorption u t u m u p dans q r n 0 t pour n 1 m p 1 avec des conditions initiales u x 0 0 pour x 0

taming griffiths singularities infinite differentiability of quenched correlation functions we prove infinite differentiability of the magnetization and of all quenched correlation functions for disordered spin systems at high temperature or strong magnetic field in the presence of griffiths singularities we also show uniqueness of the gibbs state and exponential decay of truncated correlation functions with probability one our results are obtained through new simple modified high temperature or low activity expansions whose convergence can be displayed by elementary probabilistic arguments our results require no assumptions on the probability distributions of the random parameters except for the obvious one of no percolation of infinite couplings and in the strong field situation for the also obvious requirement that zero magnetic fields do not percolate

asymptotic behavior for a singular diffusion equation with gradient absorption abstract we study the large time behavior of non negative solutions to the singular diffusion equation with gradient absorption t u p u u q 0 in 0 r n for p c 2 n n 1 p 2 and p 2 q q p n n 1 we prove that there exists a unique very singular solution of the equation which has self similar form and we show the convergence of general solutions with suitable initial data towards this unique very singular solution

an integrated control strategy to solve the disturbance decoupling problem for max plus linear systems with applications to a high throughput screening system this paper presents the new investigations on the disturbance decoupling problem ddp for the geometric control of max plus linear systems the classical ddp concept in the geometric control theory means that the controlled outputs will not be changed by any disturbances in practical manufacturing systems solving for the ddp would require further delays on the output parts than the existing delays caused by the system breakdown the new proposed modified disturbance decoupling problem mddp in this paper ensures that the controlled output signals will not be delayed more than the existing delays caused by the disturbances in order to achieve the just in time optimal control furthermore this paper presents the integration of output feedback and open loop control strategies to solve for the mddp as well as for the ddp if these controls can only solve for the mddp but not for the ddp an evaluation principle is established to compare the distance between two output signals generated by controls solving for the mddp and ddp respectively this distance can be interpreted as the number of tokens or firings that are needed in order for the controls to solve for the ddp moreover another alternative approach is finding a new disturbance mapping in order to guarantee the solvability of the ddp by the same optimal control for the mddp the main results of this paper are illustrated by using a timed event graph model of a high throughput screening system in drug discovery

correlation length bounds for disordered ising ferromagnets thed dimensional nearest neighbor disordered ising ferromagnet h sum j ij sigma i sigma j is studied as a function of both temperature t and a disorder parameter which measures the size of fluctuations of couplingsjij 0 a finite size scaling correlation length f t is defined in terms of the magnetic response of finite samples this correlation length is shown to be equivalent in the scaling sense to the quenched average correlation length t defined as the asymptotic decay rate of the quenched average two point function furthermore the magnetic response criterion which defines f is shown to have a scale invariant property at the critical point the above results enable us to prove that the quenched correlation length satisfies c left log xi t right xi t geqq left t t c right 2 mathord left vphantom 2 d right kern nulldelimiterspace d which implies the boundv 2 d for the quenched correlation length exponent

singular solutions of parabolic p laplacian with absorption we consider for and the laplacian evolution equation with absorption we are interested in those solutions which we call singular solutions that are non negative non trivial continuous in and satisfy for all we prove the following i when there does not exist any such singular solution ii when there exists for every a unique singular solution that satisfies as also as where is a singular solution that satisfies as furthermore any singular solution is either or for some finite positive

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

on the ising model with random boundary condition the infinite volume limit behavior of the 2d ising model under possibly strong random boundary conditions is studied the model exhibits chaotic size dependence at low temperatures and we prove that the and phases are the only almost sure limit gibbs measures assuming that the limit is taken along a sparse enough sequence of squares in particular we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces in order to exclude mixtures as possible limit points a detailed multi scale contour analysis is performed

on the surface pressure for the edwards anderson model for the edwards anderson model we introduce an integral representation for the surface pressure per unit surface in terms of a quenched moment of the bond overlap on the surface we consider free periodic and antiperiodic boundary conditions by symmetry and prove the bounds open image in new windowopen image in new window we show moreover that at high temperatures is close to 2 4 and is close to 2 4 uniformly in the volume