on the borel summability of planar perturbation series transition to minkowski space in recent years t hooft and rivasseau proved the borel summability of planar asymptotically free massive theories in euclidean space the corresponding borel sums in minkowski space are shown to exist as linear functionals if the euclidean counterparts are bounded polynomially in momentum space and fulfill certain analyticity conditions both can be verified in massive planar wrong sign 44 using rivasseau s approach the functionals alternatively are densely defined and unbounded on anlp space or bounded on the whole of a banach space with a more restrictive norm

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

optimal stopping of markov processes hilbert space theory approximation algorithms and an application to pricing high dimensional financial derivatives the authors develop a theory characterizing optimal stopping times for discrete time ergodic markov processes with discounted rewards the theory differs from prior work by its view of per stage and terminal reward functions as elements of a certain hilbert space in addition to a streamlined analysis establishing existence and uniqueness of a solution to bellman s equation this approach provides an elegant framework for the study of approximate solutions in particular the authors propose a stochastic approximation algorithm that tunes weights of a linear combination of basis functions in order to approximate a value function they prove that this algorithm converges almost surely and that the limit of convergence has some desirable properties the utility of the approximation method is illustrated via a computational case study involving the pricing of a path dependent financial derivative security that gives rise to an optimal stopping problem with a 100 dimensional state space

quickest sequential multiband spectrum sensing with mixed observations spectrum sensing is a key technology enabling the cognitive radio system in this paper the problem of how to quickly and accurately find an unoccupied channel from a large amount of potential channels is considered the cognitive radio system under consideration is equipped with a narrow band sensor hence it can only sense those potential channels in a sequential manner in this scenario we propose a novel two stage mixed observation sensing strategy in the first stage which is named as scanning stage the sensor observes a linear combination of the signals from a pair of channels the purpose of the scanning stage is to quickly identify a pair of channels such that at least one of them is highly likely to be unoccupied in the second stage which is called refinement stage the sensor only observers the signal from one of those two channels identified from the first stage and selects one of them as the unoccupied channel the problem under this setup is an ordered two concatenated markov stopping time problem the optimal solution is solved using the tools from the multiple stopping time theory it turns out that the optimal solution has a rather complex structure hence a low complexity algorithm is proposed to facilitate the implementation in the proposed low complexity algorithm the cumulative sum test is adopted in the scanning stage and the sequential probability ratio test is adopted in the refinement stage the performance of this low complexity algorithm is analyzed when the presence of unoccupied channels is rare numerical simulation results show that the proposed sensing strategy can significantly reduce the sensing time when the majority of potential channels are occupied

on the large order behavior of φ44 we continue the rigorous study of the large order behavior of the perturbation series for the 4 model in 4 dimensions started in 1 in this paper we prove a result announced in 1 we show that the exact radius of convergence of the borel transform of the renormalized perturbation series for 44 is greater than or equal to the expected value given by the position of the first renormalon 2 this result holds for any vector 2 2 model withn components and makes use of the lipatov bound of 1 this result is based on a partial resummation of counterterms similar to the one of 3 but in a phase space analysis of the renormalized series

renormalization proof for spontaneously broken yang mills theory with flow equations in this paper we present a renormalizability proof for spontaneously broken su 2 gauge theory it is based on flow equations i e on the wilson renormalization group adapted to perturbation theory the power counting part of the proof which is conceptually and technically simple follows the same lines as that for any other renormalizable theory the main difficulty stems from the fact that the regularization violates gauge invariance we prove that there exists a class of renormalization conditions such that the renormalized green functions satisfy the slavnov taylor identities of su 2 yang mills theory on which the gauge invariance of the renormalized theory is based

on the stability of some groups of formal diffeomorphisms by the birkhoff decomposition abstract let g be the group of one parameter identity tangent diffeomorphisms on the line whose coefficients are formal laurent series in the parameter e with a pole of finite order at 0 it is well known that the birkhoff decomposition can be defined in such a group we investigate the stability of the birkhoff decomposition in subgroups of g and give a formula for this decomposition these results are strongly related to renormalization in quantum field theory since it was proved by a connes and d kreimer that after dimensional regularization the unrenormalized effective coupling constants are the image by a formal identity tangent diffeomorphism of the coupling constants of the theory in the massless 6 3 theory this diffeomorphism is in g and its birkhoff decomposition gives directly the bare coupling constants and the renormalized coupling constants

integrable renormalization i the ladder case in recent years a hopf algebraic structure underlying the process of renormalization in quantum field theory was found it led to a birkhoff factorization for regularized hopf algebra characters i e for feynman rules in this work we would like to show that this birkhoff factorization finds its natural formulation in terms of a classical r matrix coming from a rota baxter structure underlying the target space of the regularized hopf algebra characters working in the rooted tree hopf algebra the simple case of the hopf subalgebra of ladder trees is treated in detail the extension to the general case i e the full hopf algebra of rooted trees or feynman graphs is briefly outlined

sequential and cooperative sensing for multi channel cognitive radios effective spectrum sensing is a critical prerequisite for multi channel cognitive radio cr networks where multiple spectrum bands are sensed to identify transmission opportunities while preventing interference to the primary users the present paper develops sequential spectrum sensing algorithms which explicitly take into account the sensing time overhead and optimize a performance metric capturing the effective average data rate of cr transmitters a constrained dynamic programming problem is formulated to obtain the policy that chooses the best time to stop taking measurements and the best set of channels to access for data transmission while adhering to hard collision constraints imposed to protect primary links given the associated lagrange multipliers the optimal access policy is obtained in closed form and the subsequent problem reduces to an optimal stopping problem a basis expansion based sub optimal strategy is employed to mitigate the prohibitive computational complexity of the optimal stopping policy a novel on line implementation based on the recursive least squares rls algorithm along with a stochastic dual update procedure is then developed to obviate the lengthy training phase of the batch scheme cooperative sequential sensing generalizations are also provided with either raw or quantized measurements collected at a central processing unit the numerical results presented verify the efficacy of the proposed algorithms

the strong coupling expansion and the ultra local approximation in field theory abstract we first discuss the strong coupling expansion in 4 d theory and quantum electrodynamics in a d dimensional euclidean space in a formal representation for the schwinger functional we treat the gaussian part of the action as a perturbation with respect to the remaining terms in this way we develop a perturbative expansion around the ultra local model where fields defined at different points of euclidean space are decoupled we examine the singularities of the strong coupling perturbative expansion analysing the analytic structure of the zero dimensional generating functions in the coupling constant complex planes we also discuss the ultra local generating functional in a non polynomial model in field theory defined by the following interaction lagrangian density l ii g 1 g 2 g 1 cosh g 2 x 1 finally we use the strong coupling perturbative expansion to compute the renormalized vacuum energy of the strongly coupled 4 d theory assuming that the scalar field is defined in a region bounded by two parallel hyperplanes where we are imposing dirichlet dirichlet boundary conditions

autocorrelation based decentralized sequential detection of ofdm signals in cognitive radios this paper introduces a simple and computationally efficient spectrum sensing scheme for orthogonal frequency division multiplexing ofdm based primary user signal using its autocorrelation coefficient further it is shown that the log likelihood ratio test llrt statistic is the maximum likelihood estimate of the autocorrelation coefficient in the low signal to noise ratio snr regime performance of the local detector is studied for the additive white gaussian noise awgn and multipath channels using theoretical analysis obtained results are verified in simulation the performance of the local detector in the face of shadowing is studied by simulations a sequential detection sd scheme where many secondary users cooperate to detect the same primary user is proposed user cooperation provides diversity gains as well as facilitates using simpler local detectors the sequential detection reduces the delay and the amount of data needed in identification of the underutilized spectrum the decision statistics from individual detectors are combined at the fusion center fc the statistical properties of the decision statistics are established the performance of the scheme is studied through theory and validated by simulations a comparison of the sd scheme with the neyman pearson fixed sample size fss test for the same false alarm and missed detection probabilities is also carried out

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

borel summability of the 1 n expansion for then vector o n non linear σ models we construct an analytic interpolation in 1 n for then vector o n non linear models withn component fields on a lattice this interpolation valid at sufficiently high temperatures extends over a large domain in the complex plane containing the half plane re 1 n 0 we use this result to show that the 1 n expansion of the free energy density and of the correlation functions is borel summable in the thermodynamic limit and at high temperature

renormalization in quantum field theory and the riemann hilbert problem i the hopf algebra structure of graphs and the main theorem this paper gives a complete selfcontained proof of our result announced in 6 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the riemann hilbert problem we shall first show that for any quantum field theory the combinatorics of feynman graphs gives rise to a hopf algebra which is commutative as an algebra it is the dual hopf algebra of the enveloping algebra of a lie algebra whose basis is labelled by the one particle irreducible feynman graphs the lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa the corresponding lie group g is the group of characters of we shall then show that using dimensional regularization the bare unrenormalized theory gives rise to a loop where c is a small circle of complex dimensions around the integer dimension d of space time our main result is that the renormalized theory is just the evaluation at z d of the holomorphic part of the birkhoff decomposition of we begin to analyse the group g and show that it is a semi direct product of an easily understood abelian group by a highly non trivial group closely tied up with groups of diffeomorphisms the analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title

on the local borel transform of perturbation theory we prove existence of the local borel transform for the perturbative series of massive varphi 4 4 theory as compared to previous proofs in the literature the present bounds are much sharper as regards the dependence on external momenta they are explicit in the number of external legs and they are obtained quite simply through a judiciously chosen induction hypothesis applied to the wegner wilson polchinski flow equations we pay attention not to generate an astronomically large numerical constant for the inverse radius of convergence of the borel transform

some classes of renormalizable tensor models we identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property mainly a version of the rank 3 tensor model as defined by ben geloun and samary ann henri poincare 14 1599 2013 e print arxiv 1201 0176 hep th 10 1007 s00023 012 0225 5 and the grosse wulkenhaar model in 4d and 2d generate three different classes of renormalizable models the proof of the renormalizability is fully performed for the first reduced model the same procedure can be applied for the remaining cases interestingly we find that due to the peculiar behavior of anisotropic wave function renormalizations the rank 3 tensor model reduced to a matrix model generates a simple super renormalizable vector model

the lipatov argument for φ 3 4 perturbation theory we extend to 3 4 the work of s breen on the leading behavior at large order of 2 4 perturbation theory using a phase space expansion to obtain new estimates on the high energy behavior of 3 4 feynman graphs and a rigorous semiclassical expansion we prove that the radius of convergence of the borel transform of the pertubative series for 3 4 euclidean field theory is the one computed by the lipatov method

isosystolic inequalities and the topological expansion for random surface and matrix models using the isosystolic inequalities on riemann surfaces we prove that for many random surface or matrix models the radius of convergence of the perturbative series at fixed genus is independent of the genus this result applies for instance to the dynamically triangulated random surface model in any dimension or to many matrix models with regular propagators in the superrenormalizable domain for instance 3 in dimensiond 6 lambda phi 4 sqrt lambda phi 3 in dimensiond 4 and various otherp 2 models in particular all those containing an odd power of we hope that this result is a first step towards a more rigorous understanding of the genus dependence of surface models or of quantum gravity coupled with matter fields

borel summability in the disorder parameter of the averaged green s function for gaussian disorder in this note we prove borel summability in the disorder parameter of the averaged green s function y of tight binding models h v delta v with gaussian disorder d lambda v 2 pi gamma 1 2 exp v 2 2 gamma dv for 0 and fixed large e using this we can reconstruct the density of states e from the borel sums of y with ime 0 and ime 0

dimensional regularization and renormalization of qed we give an space definition of dimensional regularization suited to the tree expansion method of renormalization we apply the dimensionally regularized tree expansion to qed obtaining sharp bounds on the size of a renormalized graph subtractions are made with the lagrangian counterterms of the tree expansion not by minimal subtraction techniques and so do not entail a knowledge of the meromorphic structure of a graph as a function of dimension this renormalization procedure respects the ward identities and the counterterms required are gauge invariant

renormalization in the complete mellin representation of feynman amplitudes the feynman amplitudes are renormalized in the formalism of the cm representation this mellin barnes type integral representation previously introduced for the study of asymptotic behaviours is shown to have the following interesting property in contrast with the usual subtraction procedures the renormalization leaves the cm integrand unchanged and only results into translations of the integration path the explicit cm representation of the renormalized amplitudes is given in addition the dimensional regularization and the extension to spinor amplitudes are sketched

perturbation theory and non renormalizable scalar fields we study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of p d when one does not allow any renormalization besides the usual coupling constants mass and wave function renormalizations

a renormalization group proof of perturbative renormalizability this paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean 4 4 theory its aim is partly pedagogical by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages the present version is based on the renormalized tree expansion adapted to the continuous renormalization group all detailed results are proved by induction on the size of the tree the continuous rg version presented here has one big advantage over the discrete rg version discussed elsewhere in the continuous version a tree has a more restrictive structure there is a one to one correspondence between forks of the tree and lines of feynman graphs this extra structure eliminates the need to introduce feynman graphs in the first place it also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

renormalization in quantum field theory and the riemann hilbert problem ii the β function diffeomorphisms and the renormalization group we showed in part i that the hopf algebra of feynman graphs in a given qft is the algebra of coordinates on a complex infinite dimensional lie group g and that the renormalized theory is obtained from the unrenormalized one by evaluating at 0 the holomorphic part of the riemann hilbert decomposition 1 of the loop g provided by dimensional regularization we show in this paper that the group g acts naturally on the complex space x of dimensionless coupling constants of the theory more precisely the formula g 0 gz 1 z 3 3 2 for the effective coupling constant when viewed as a formal power series does define a hopf algebra homomorphism between the hopf algebra of coordinates on the group of formal diffeomorphisms to the hopf algebra this allows first of all to read off directly without using the group g the bare coupling constant and the renormalized one from the riemann hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms this shows that renormalization is intimately related with the theory of non linear complex bundles on the riemann sphere of the dimensional regularization parameter it also allows to lift both the renormalization group and the function as the asymptotic scaling in the group g this exploits the full power of the riemann hilbert decomposition together with the invariance of under a change of unit of mass this not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group g for the full higher pole structure of minimal subtracted counterterms in terms of the residue

estimation of primary user parameters in cognitive radio systems via hidden markov model for a cognitive radio cr system we investigate the estimation problem in which a secondary user su estimates the channel parameters such as the sojourn times on the active and the inactive states of the primary user pu as well as the pu signal strength on the basis of the sequence of the sensing results by modeling the cr system as a hidden markov model hmm the channel parameters are estimated by the standard expectation maximization em algorithm we focus on mathematically analyzing the condition under which the em algorithm can find the true channel parameters for this we apply the theory of the equivalence and the identifiability to the proposed hmm model for a cr system based on the identifiability analysis we propose a parameter estimation algorithm for our problem by extending the em algorithm the numerical results show that the proposed algorithm successfully estimates the true channel parameters as long as the condition for finding the channel parameters is satisfied

from dynamical systems to renormalization in this paper we study logarithmic derivatives associated to derivations on completed graded lie algebra as well as the existence of inverses these logarithmic derivatives when invertible generalize the exp log correspondence between a lie algebra and its lie group such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non linearizability of a resonant vector fields corresponds to the non invertibility of a logarithmic derivative and to the existence of normal forms these concepts stemming from the theory of dynamical systems can be rephrased in the abstract setting of lie algebra and the same difficulties as in perturbative quantum field theory pqft arise here surprisingly one can adopt the same ideas as in pqft with fruitful results such as new constructions of normal forms with the help of the birkhoff decomposition the analogy goes even further locality of counter terms choice of a renormalization scheme and shall lead to more interactions between dynamical systems and quantum field theory

distributed structures sequential optimization and quantization for detection in the design of distributed quantization systems one inevitably confronts two types of constraints those imposed by a distributed system s structure and those imposed by how the distributed system is optimized structural constraints are inherent properties of any distributed quantization system and are normally summarized by functional relationships defining the inputs and outputs of their component quantizers the use of suboptimal optimization methods are often necessitated by the computational complexity encountered in distributed problems this correspondence briefly explores the impact and interplay of these two types of constraints in the context of distributed quantization for detection we introduce two structures that exploit interquantizer communications and that represent extremes in terms of their structural constraints we then develop a sequential optimization scheme that maximizes the kullback leibler divergence takes advantage of statistical dependencies in the distributed system s output variables and leads to simple parameterizations of the component quantization rules we present an illustrative example from which we draw insights into how these constraints influence the quantization boundaries and affect performance relative to lower and upper bounds

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

a lipatov bound for φ 4 4 euclidean field theory we bound the large order behavior of these pieces of the renormalized perturbation expansion for 4 4 which do not contain renormalons 1 the bound we obtain has the form of the leading asymptotic behavior computed by the lipatov method with the exact value of the lipatov constant therefore this paper is a step towards the rigorous study of the large order behavior of 4 4 and towards a proof of existence of the first renormalon singularity which should prevent the theory from being borel summable using the results of this paper and the techniques of 15 one can for instance improve 17 the estimate 18 on the finiteness of the radius of convergence of the borel transform of renormalized 4 4 and obtain that this radius is at least the exact value conjectured in 1

on the convergence of planar diagram expansions renormalizable quantum field theories whose perturbation expansions are described by planar feynman diagrams only such as su gauge theory are considered in 4 dimensional euclidean space for studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs in this paper it is proved that this infinite set of diagrams when summed converges within a finite radius of convergence for the coupling constant

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model

local existence of the borel transform in euclidean massless φ 4 4 we extend the methods of 1 to prove large order estimates on the renormalized feynman amplitudes of massless 4 4 euclidean field theory at non exceptional momenta the borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane this result is a step towards the rigorous investigation of the infra red singularities in the borel plane for theories containing massless particles like the gauge theories

the scaling limit of the energy correlations in non integrable ising models we obtain an explicit expression for the multipoint energy correlations of a non solvable two dimensional ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory which generalizes the one originally used by schultz mattis and lieb for the nearest neighbor ising model the interacting model is then analyzed by a multiscale method first proposed by pinson and spencer if the lattice spacing is finite then the correlations cannot be computed in closed form rather they are expressed in terms of infinite convergent power series in in the scaling limit these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable ising model up to a finite renormalization of the parameters explicit bounds on the speed of convergence to the scaling limit are derived

bounds on completely convergent euclidean feynman graphs letg be a euclidean feynman graph containingl g lines we prove that ifg has massive propagators and does not contain any divergent subgraphs its value is bounded bykl g we also prove the infrared analogue of this bound

fast multiband spectrum scanning for cognitive radio systems this paper considers the problem of how to quickly and accurately determine the availability of each spectrum band for a multi band primary system using one or few sensors such problem is referred to as spectrum scanning two cases of practical interest are studied 1 a single sensor case in which only one spectrum band is observed at one time and 2 a multiple sensor case in which multiple spectrum bands are observed simultaneously for each case scenarios with and without a scanning delay constraint are investigated using mathematical tools from optimal stopping theory optimal spectrum scanning algorithms are developed to minimize a cost function that strikes a desirable trade off between detection performance and sensing delay in the non delay constrained case it is shown that the optimal scanning algorithm is a concatenated sequential probability ratio test c sprt in the delay constrained case the optimal scanning algorithm has a high implementation complexity and truncation algorithms are developed as alternative low complexity options numerical examples are provided to illustrate the effectiveness of the proposed algorithms

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

the equations for the moduli space of n points on the line a central question in invariant theory is that of determining the relations among invariants geometric invariant theory git quotients come with a natural ample line bundle and hence often a natural projective embedding this question translates to determining the equations of the moduli space under this embedding this article deals with one of the most classical quotients the space of ordered points on the projective line we show that under any weighting of the points this quotient is cut out scheme theoretically by a particularly simple set of quadric relations with the single exception of the segre cubic threefold the space of six points with equal weight we also show that the ideal of relations is generated in degree at most four and we give an explicit description of the generators if all the weights are even e g in the case of equal weight for odd n then we show that the ideal of relations is generated by quadrics

cooperative sequential spectrum sensing based on level triggered sampling we propose a new framework for cooperative spectrum sensing in cognitive radio networks that is based on a novel class of nonuniform samplers called the event triggered samplers and sequential detection in the proposed scheme each secondary user su computes its local sensing decision statistic based on its own channel output and whenever such decision statistic crosses certain predefined threshold values the secondary user will send one or several bit of information to the fusion center fc the fc asynchronously receives the bits from different sus and updates the global sensing decision statistic to perform a sequential probability ratio test sprt to reach a sensing decision we provide an asymptotic analysis for the above scheme and under different conditions we compare it against the cooperative sensing scheme that is based on traditional uniform sampling and sequential detection simulation results show that the proposed scheme using even 1 bit can outperform its uniform sampling counterpart that uses infinite number of bits under changing target error probabilities snr values and number of sus

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

the random walk representation of classical spin systems and correlation inequalities ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion by using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities as an application of these inequalities we obtain a simple proof of the mass gap for the 4 2 quantum field model we also establish new upper bounds on critical temperatures

hopf algebras renormalization and noncommutative geometry we explore the relation between the hopf algebra associated to the renormalization of qft and the hopf algebra associated to the ncg computations of tranverse index theory for foliations

hopf algebraic structure of families of trees in this paper we describe hopf algebras which are associated with certain families of trees these hopf algebras originally arose in a natural fashion one of the authors 5 was investigating data structures based on trees which could be used to efficiently compute certain differential operators given data structures such as trees which can be multiplied and which act as higherorder derivations on an algebra one expects to find a hopf algebra of some sort we were pleased to find that not only was there a hopf algebra associated with these data structures but that it could be used to give new proofs of enumerations of such objects as rooted trees and ordered rooted trees previous work applying hopf algebras to combinatorial objects such as 10 13 or 14 has concerned itself with algebraic structures on polynomial algebras and on partially ordered sets rather than on trees themselves

phase space analysis and particle structure in field theory progress in the last few years in constructive field theory has included 1 the construction of three dimensional non abelian gauge theories in a finite volume 2 the construction of models that are asymptotically free or have a nontrivial fixed point 3 a new presentation of perturbation theory yielding old and new large order estimates and 4 asymptotic completeness for renormalizable models in the two particle region the existence of multiparticle structure equations in the euclidean region provided that the coupling constant goes to zero as the energy increases these equations yield formally the asymptotic completeness in obtaining most of these results the phase space expansion pioneered by glimm and jaffe plays a crucial role the first part of this review is a description of the phase space expansion in the ecole polytechnique version the second part is devoted to the construction of models the third part treats perturbation theory and the last part deals with asymptotic completeness

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

renormalization group approach to lattice gauge field theories i generation of effective actions in a small field approximation and a coupling constant renormalization in four dimensions on etudie des theories de champs de jauge pures a 4 dimensions par l approche du groupe de renormalisation on se restreint a l approximation de champ petit dans cette region on construit une suite d actions effectives localisees par des developpements en amas dans des transformations de renormalisation a un pas

analyticity of the density of states and replica method for random schrodinger operators on a lattice we analyze the density of states and some aspects of the replica method for anderson s tight binding model on a lattice of arbitrary dimension with diagonal disorder we give heuristic arguments for the conjectures that the classical value of the exponent of the localization length is 1 2 and that the upper critical dimension d c loc is bounded by 4 d c loc 6

perturbative renormalization of composite operators via flow equations i we apply the general framework of the continuous renormalization group whose significance for perturbative quantum field theories was recognized by polchinski to investigate by new and mathematically simple methods the perturbative renormalization of composite operators in this paper we demonstrate the perturbative renormalizability of the green functions of the euclidean massive 44 theory with one insertion of a possibly oversubtracted in the bphz language composite operator moreover we show that our method admits an easy proof of the zimmermann identities and of the lowenstein rule

an algebraic birkhoff decomposition for the continuous renormalization group this paper aims at presenting the first steps towards a formulation of the exact renormalization group equation in the hopf algebra setting of connes and kreimer it mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations the relation between renormalization formulated as a change of boundary condition for a differential equation and an algebraic birkhoff decomposition for rooted trees is explicited

local borel summability of euclidean 311 1311 1311 1a simple proof via differential flow equations it is shown how the differential flow equation or equivalently the continous renormalization group method can be employed to give an astonishingly easy proof of the local borel summability of the renormalized perturbative euclidean massive 44

rigorous construction of planar diagram field theories in four dimensional euclidean space asymptotically free quantum field theories with planar feynman diagrams such as su gauge theory are considered in 4 dimensional euclidean space it is shown that if all particles involved have non vanishing masses and if the coupling constant s org2 are small enough crit then an absolutely convergent procedure exists to obtain green functions that uniquely solve the dyson schwinger equations