uniform convergence of the free energy of the classical heisenberg model to that of the gaussian model we show that the free energy of the classical heisenberg model converges to the free energy of the gaussian in the low temperature limit the limit is uniform as the field is taken to zero

existence and roughness of exponential dichotomies of linear dynamic equations on time scales in this paper we define the exponential dichotomy of linear dynamic equations on time scales then we present perturbation theorems on the roughness of exponential dichotomy and develop several explicit sufficient criteria for linear dynamic equations to have an exponential dichotomy as applications of the criteria of exponential dichotomy we derive some new sufficient conditions for the existence of periodic solutions of semi linear dynamic equations and nonlinear dynamic equations on time scales

dichotomies and asymptotic solutions of nonlinear differential systems the problem of asymptotic equivalence between two systems of ordinary differential equations has been studied by many authors l 5 it was first used by levinson in his theorem on asymptotic integration 6 71 in l 51 this problem is studied when system 1 2 is stable a t is constant and g t y b t is integrable in 3 theorems 5 111 it is assumed that the linear system 1 2 has an ordinary dichotomy and the nonlinear term g t y is lipschitz continuous in 2 the previous results are extended to nonlinear perturbations g t y which are not lipschitz continuous such that g t y l i r t y where r t y is monotone in y we emphasize that in all these works only the asymptotic equivalence between bounded solutions is established nothing is said about a possible correspondence between unbounded solutions of 1 1 and 1 2 in this paper we suppose that the nonlinear term g t y satisfies some integrability conditions that we summarize in hypothesis h2 these conditions permit one to consider systems with large nonlinearities for example equations where g t y is an oscillatory function of the variable y no lipschitz conditions or monotonicity properties are required of g t y however we will use dichotomic properties of system 1 2

exponential dichotomy roughness and structural stability for evolution families without bounded growth and decay abstract we show that if u t s is an exponentially dichotomic evolution operator then the unique solution of the volterra equation v t s u t s s t u t b v s d is also an exponentially dichotomic evolution operator for small b t as a consequence we prove that any exponentially dichotomic evolution family is structurally stable we improve the previous results showing that the condition of bounded growth and decay present everywhere in the existing literature can be completely removed

lyapunov functions for strong exponential contractions abstract our main aim is to give a complete characterization of an exponential contraction in terms of lyapunov sequences for discrete time or lyapunov functions for continuous time in particular we obtain inverse theorems giving explicitly a quadratic lyapunov function for each exponential contraction we consider the general cases of 1 nonautonomous dynamics either obtained from a product of linear operators or from a nonautonomous differential equation respectively for discrete and continuous time 2 nonuniform exponential contractions in which the uniform stability is replaced by a nonuniform stability 3 strong exponential behavior in the sense that we have simultaneously lower and upper contraction bounds we emphasize that the two last properties are ubiquitous in the context of ergodic theory and in particular for almost all trajectories of any measure preserving flow which justifies completely the study of this general type of exponential behavior as a nontrivial application of our work we establish the robustness of any strong nonuniform exponential contraction that is the persistence of the asymptotic stability of a strong nonuniform exponential contraction under sufficiently small linear perturbations

robustness of discrete dynamics via lyapunov sequences for a nonautonomous dynamics with discrete time defined by a sequence of matrices we give a complete characterization of nonuniform exponential contractions and nonuniform exponential dichotomies in terms of lyapunov sequences we note that these include as very special cases uniform exponential contractions and uniform exponential dichotomies due to the central role played by these properties in a substantial part of the theory of dynamical systems in particular in connection with the study of stable and unstable invariant manifolds it is important to have available optimal characterizations that are more amenable to check whether a given dynamics has such a property we also obtain inverse theorems that give explicitly lyapunov sequences for a given contraction or dichotomy as a nontrivial application we establish the robustness under sufficiently small linear perturbations both of nonuniform exponential contractions and nonuniform exponential dichotomies we emphasize that when compared to former work our proof of the robustness property is much simpler

lyapunov functions for trichotomies with growth rates abstract we consider linear equations x a t x that may exhibit stable unstable and central behaviors in different directions with respect to arbitrary asymptotic rates e c t determined by a function t for example the usual exponential behavior with t t is included as a very special case and when t log t we obtain a polynomial behavior we emphasize that we also consider the general case of nonuniform exponential behavior which corresponds to the existence of what we call a nonuniform exponential trichotomy this is known to occur in a large class of nonautonomous linear equations our main objective is to give a complete characterization in terms of strict lyapunov functions of the linear equations admitting a nonuniform exponential trichotomy this includes criteria for the existence of a nonuniform exponential trichotomy as well as inverse theorems providing explicit strict lyapunov functions for each given exponential trichotomy in the particular case of quadratic lyapunov functions we show that the existence of strict lyapunov sequences can be deduced from more algebraic relations between the quadratic forms defining the lyapunov functions as an application of the characterization of nonuniform exponential trichotomies in terms of strict lyapunov functions we establish the robustness of nonuniform exponential trichotomies under sufficiently small linear perturbations we emphasize that in comparison with former works our proof of the robustness is much simpler even when t t

smooth robustness of parameterized perturbations of exponential dichotomies we establish the robustness of nonuniform exponential dichotomies in banach spaces under sufficiently small c1 parameterized perturbations moreover we show that the stable and unstable subspaces of the exponential dichotomies obtained from the perturbation are also of class c1 on the parameter thus yielding an optimal smoothness

a topological classification of linear differential equations on banach spaces abstract in the present work we give necessary and sufficient conditions for linear differential non autonomous equations on a banach space that satisfy exponential dichotomy to be topologically equivalent we shall also prove that such equations are structurally stable

robust nonuniform dichotomies and parameter dependence abstract we establish the robustness of linear cocycles with an exponential dichotomy under sufficiently small lipschitz perturbations in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations we consider cocycles in banach spaces as well as the general case of nonuniform exponential dichotomies and also the general case of an exponential behavior e c n given by an arbitrary sequence n including the usual exponential behavior n n as a very special case moreover we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter and in fact that they are locally lipschitz on finite dimensional parameters

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

nonuniform h k μ ν dichotomy with applications to nonautonomous dynamical systems the paper develops and studies a very general notion of dichotomy referred to as nonuniform h k dichotomy the new notion contains as special cases most versions of dichotomy existing in the literature the paper then provides corresponding new versions of robustness hartman grobman theorem and stable manifold theorem for nonautonomous dynamical systems in banach spaces in term of the nonuniform h k dichotomy

robustness via lyapunov functions for nonautonomous linear equations x a t x we give a complete characterization of nonuniform exponential dichotomies in terms of strict quadratic lyapunov functions nonuniform exponential dichotomies include as a very special case uniform exponential dichotomies in particular we construct explicitly strict lyapunov functions for each exponential dichotomy as a nontrivial application we establish in a simple and direct manner the robustness of nonuniform exponential dichotomies under sufficiently small linear perturbations this represents a considerable simplification of former work

harnack s inequality and holder continuity for weak solutions of degenerate quasilinear equations with rough coefficients abstract we continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form div a x u u b x u u for x as considered in our paper monticelli et al 2012 there we proved only local boundedness of weak solutions here we derive a version of harnack s inequality as well as local holder continuity for weak solutions the possible degeneracy of an equation in the class is expressed in terms of a nonnegative definite quadratic form associated with its principal part no smoothness is required of either the quadratic form or the coefficients of the equation our results extend ones obtained by j serrin 1964 and n trudinger 1967 for quasilinear equations as well as ones for subelliptic linear equations obtained in sawyer and wheeden 2006 2010

exponential dichotomy and trichotomy for difference equations abstract in this paper a roughness theorem of exponential dichotomy and trichotomy of linear difference equations is proved it is also shown that if an almost periodic difference equation has an exponential dichotomy on a sufficiently long finite interval then it has one on

a low temperature expansion for classical n vector models iii a complete inductive description fluctuation integrals we give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical n vector models described in the paper 1 and we formulate the main theorems of this sequence of papers this description includes now all the large field domains which we ve excluded from the discussions of 1 4 we apply the renormalization transformation to a density satisfying the inductive hypotheses we introduce large field small field partitions and we determine and analyze the fluctuation integrals in the general setting

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

robustness of nonuniform μ ν dichotomies in banach spaces abstract this paper focuses on the linear perturbation of dynamical systems in banach spaces which corresponds to a nonautonomous dynamical system admitting a nonuniform dichotomy we establish the robustness or roughness of nonuniform dichotomies in the sense that the linear dynamical system persists under a sufficiently small linear perturbation

on admissible perturbations for exponential dichotomy in this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite dimensional banach spaces unlike some previous works we do not assume bounded growth we consider linear non autonomous ordinary differential equations with bounded and unbounded coefficients

existence and robustness of nonuniform h k μ ν dichotomies for nonautonomous impulsive differential equations abstract for the linear nonautonomous impulsive differential equation we propose a new notion called the nonuniform h k dichotomy which extends the notion of dichotomy of uniform and nonuniform types and is related to the theory of nonuniform hyperbolicity we establish a sufficient criterion for the existence of the nonuniform h k dichotomy in terms of appropriate lyapunov exponents for the linear perturbation we develop the robustness or roughness of nonuniform h k dichotomies in the sense that a nonuniform h k dichotomy persists under a sufficiently small linear perturbation

lattice systems with a continuous symmetry iii low temperature asymptotic expansion for the plane rotator model we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

second order elliptic equations with variably partially vmo coefficients abstract the solvability in w p 2 r d spaces is proved for second order elliptic equations with coefficients which are measurable in one direction and vmo in the orthogonal directions in each small ball with the direction depending on the ball this generalizes to a very large extent the case of equations with continuous or vmo coefficients

weighted and regularity estimates for nonlinear equations on reifenberg flat domains abstract global weighted l p estimates are obtained for the gradient of solutions to nonlinear elliptic dirichlet boundary value problems over a bounded nonsmooth domain morrey and holder regularity of solutions are also established as a consequence these results generalize various existing estimates for nonlinear equations the nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation the boundary of the domain on the other hand may exhibit roughness but assumed to be sufficiently flat in the sense of reifenberg our approach uses maximal function estimates and vitali covering lemma and also known regularity results of solutions to nonlinear homogeneous equations

boundary estimates for solutions to linear degenerate parabolic equations let omega subset mathbb r n be a bounded nta domain and let omega t omega times 0 t for some t 0 we study the boundary behaviour of non negativesolutions to the equation hu parti

robustness of general dichotomies abstract for a linear equation v a t v we consider general dichotomies that may exhibit stable and unstable behaviors with respect to arbitrary asymptotic rates e c t for some function t this includes as a special case the usual exponential behavior when t t we also consider the general case of nonuniform exponential dichotomies we establish the robustness of the exponential dichotomies in banach spaces in the sense that the existence of an exponential dichotomy for a given linear equation persists under sufficiently small linear perturbations we also establish the continuous dependence with the perturbation of the constants in the notion of dichotomy

exponential dichotomy roughness on banach spaces in the present paper we extend existing results on exponential dichotomy roughness for linear ode systems to infinite dimensional banach space we give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case we also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

roughness of tempered exponential dichotomies for infinite dimensional random difference equations abstract in this paper we study the roughness of tempered exponential dichotomies for linear random dynamical systems in banach spaces such a dichotomy has a tempered bound and describes nonuniform hyperbolicity we prove the roughness without assuming their invertibility and the integrability condition of the multiplicative ergodic theorem we give an explicit bound for the linear perturbation such that the dichotomy is persistent we also obtain explicit forms for the exponent and the bound of tempered exponential dichotomy of the perturbed random system in terms of the original ones and the perturbations

robustness of nonuniform exponential trichotomies in banach spaces abstract we establish the robustness under sufficiently small linear perturbations of nonuniform exponential trichotomies defined by linear equations x a t x in banach spaces we also establish the continuous dependence on the perturbation of the constants in the notion of trichotomy we consider both trichotomies in semi infinite intervals and trichotomies in r

elliptic equations in divergence form with partially bmo coefficients the solvability in sobolev spaces is proved for divergence form second order elliptic equations in the whole space a half space and a bounded lipschitz domain for equations in the whole space or a half space the leading coefficients aij are assumed to be only measurable in one direction and have locally small bmo semi norms in the other directions for equations in a bounded domain additionally we assume that aij have small bmo semi norms in a neighborhood of the boundary of the domain we give a unified approach of both the dirichlet boundary problem and the conormal derivative problem we also investigate elliptic equations in sobolev spaces with mixed norms under the same assumptions on the coefficients

strong nonuniform behaviour a datko type characterization abstract we obtain a datko type characterization of several classes of a strong nonuniform exponential behaviour we consider separately the case of exponential contractions expansions and dichotomies in addition we consider both discrete and continuous time as a nontrivial application of our work we study the robustness property of strong nonuniform exponential contractions expansions and dichotomies

elliptic equations with measurable nonlinearities in nonsmooth domains abstract we study elliptic equations with measurable nonlinearities in nonsmooth domains we establish an optimal global w 1 p estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small bmo semi norm in the other variables while the underlying domain is sufficiently flat in the reifenberg sense that the boundary of the domain is locally trapped between two narrow strips

exact bounds for exponential dichotomy roughness iii semistrong dichotomy abstract in this part we extend the results of part i by eliminating the restriction of orthogonality of the unperturbed subspaces or even of a constant angle between them we shall call this case semistrong dichotomy

weighted w1 p estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable abstract this paper studies sobolev regularity of weak solution of degenerate elliptic equations in divergence form div a x u div f x where x x y r n r the coefficient matrix a x is a symmetric measurable n 1 n 1 matrix and it could be degenerate or singular in the one dimensional y variable as a weight function in the a 2 muckenhoupt class our results give weighted sobolev regularity estimates of calderon zygmund type for weak solutions of this class of degenerate singular equations as an application of these estimates we establish global fractional sobolev regularity estimates for solutions of the spectral fractional elliptic equation with measurable coefficients this result can be considered as the sobolev counterpart of the recently established schauder regularity theory of fractional elliptic equations

lattice systems with a continuous symmetry we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

roughness of h k dichotomies abstract in this paper we prove a roughness theorem for a class of dichotomies of linear systems of differential equations the so called h k dichotomies these include a great variety of dichotomies among them the ordinary and exponential dichotomies exponential ordinary dichotomies levinson dichotomies for diagonal systems etc we prove that under general uniform conditions upon the functions h and k these dichotomies are not destroyed by integrable perturbations this result generalizes the property of roughness of ordinary dichotomies under integrable perturbations

exponential dichotomy integral separation and diagonalizability of linear systems of ordinary differential equations abstract this paper is concerned with linear systems of ordinary differential equations a criterion for integral separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half line is integrally separated if and only if the system corresponding to its diagonal is we then show that a diagonal system on a half line is integrally separated if and only if a certain perturbed system is diagonalizable using this result we are able to deduce that the interior of the set of diagonalizable systems on a half line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half lines

robustness of nonuniform exponential dichotomies in banach spaces we give conditions for the robustness of nonuniform exponential dichotomies in banach spaces in the sense that the existence of an exponential dichotomy for a given linear equation x a t x persists under a sufficiently small linear perturbation we also establish the continuous dependence with the perturbation of the constants in the notion of dichotomy and of the angles between the stable and unstable subspaces our proofs exhibit implicitly the exponential dichotomies of the perturbed equations in terms of fixed points of appropriate contractions we emphasize that we do not need the notion of admissibility of bounded nonlinear perturbations we also obtain related robustness results in the case of nonuniform exponential contractions in addition we establish an appropriate version of robustness for nonautonomous dynamical systems with discrete time

nonuniform behavior and robustness we establish the robustness of linear cocycles in banach spaces admitting a nonuniform exponential dichotomy we first obtain robustness results for positive and negative time by establishing exponential behavior along certain subspaces and showing that the associated sequences of projections have bounded exponential growth we then establish a robustness result in z by constructing explicitly appropriate projections on the stable and unstable subspaces we emphasize that in general these projections may be different from those obtained separately from the robustness for positive and negative time we also consider the case of strong nonuniform exponential dichotomies

parabolic equations with bmo coefficients in lipschitz domains abstract in this paper we are concerned with certain natural sobolev type estimates for weak solutions of inhomogeneous problems for second order parabolic equations in divergence form the geometric setting is that of time independent cylinders having a space intersection assumed to be locally given by graphs with small lipschitz coefficients the constants of the operator being uniformly parabolic we prove the relevant l p estimates assuming that the coefficients are in parabolic bounded mean oscillation bmo and that their parabolic bmo semi norms are small enough

on the error in qr integration an important change of variables for a linear time varying system dot x a t x t ge 0 is that induced by the qr factorization of the underlying fundamental matrix solution x qr with q orthogonal and r upper triangular with positive diagonal to find this change of variable one needs to solve a nonlinear matrix differential equation for q practically this means finding a numerical approximation to q by using some appropriate discretization scheme whereby one attempts to control the local error during the integration our contribution in this work is to obtain global error bounds for the numerically computed q these bounds depend on the local error tolerance used to integrate for q and on structural properties of the problem itself but not on the length of the interval over which we integrate this is particularly important since in principle q may need to be found on the half line t ge 0

positive solutions of nonlinear problems involving the square root of the laplacian abstract we consider nonlinear elliptic problems involving a nonlocal operator the square root of the laplacian in a bounded domain with zero dirichlet boundary conditions for positive solutions to problems with power nonlinearities we establish existence and regularity results as well as a priori estimates of gidas spruck type in addition among other results we prove a symmetry theorem of gidas ni nirenberg type

a characterization of exponential separation in terms of reducibility for linear difference equations abstract the main aim of this paper is to show that a linear difference equation is exponentially separated if and only if all neighboring equations are reducible

computing spectral bounds of the heisenberg ferromagnet from geometric considerations we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperimetric problem holds then our proposed method of estimating the energy eigenvalues via approximating the edge isoperimetric properties of vertex induced subgraphs will yield a polynomial time algorithm for estimating the smaller energy eigenvalues of the heisenberg ferromagnet we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperi

nonlinear commutators for the fractional p laplacian and applications we prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p laplacian this implies that solutions to certain degenerate nonlocal equations are higher differentiable also weakly fractional p harmonic functions which a priori are less regular than variational solutions are in fact classical as an application we show that sequences of uniformly bounded frac n s harmonic maps converge strongly outside at most finitely many points

exponential separation exponential dichotomy and spectral theory for linear systems of ordinary differential equations abstract this paper is concerned with linear nonautonomous systems of ordinary differential equations a criterion for exponential separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for exponential separation and the new result that an upper triangular system on a half line is exponentially separated if and only if the system corresponding to its diagonal is a minimal decomposition into exponentially separated subspaces is defined it turns out that it is in general finer than the sacker sell spectral decomposition but that the two decompositions coincide for almost periodic systems

on asymptotic limits for the quantum heisenberg model the authors discuss various asymptotic limits of the classical and quantum heisenberg model they give a new proof that the thermodynamic free energy of the quantum model converges to the free energy of the classical model in the limit of large spins they also obtain gaussian and free bose gas limits for the classical and quantum models respectively

on roughness of exponential dichotomy we present new perturbation theorems on the roughness of exponential dichotomy which improve previous results the proofs given here are also much simpler compared with previous ones the new results provide significant improvements of existing results in the case where the operator a t is unbounded for t j this is precisely the situation that is of interest from the point of view of the applications in lobe dynamics the results are also valid in banach spaces and useful for general purposes

random walk representations of the heisenberg model we develop random walk representations for the spin s heisenberg ferromagnet with nearest neighbor interactions we show that the spin s heisenberg model is a diffusion with local times controlled by the spin s ising model as a consequence expectations for the heisenberg model conditioned on zero diffusion are shown to be ising expectations

proof of aldous spectral gap conjecture aldous spectral gap conjecture asserts that on any graph the random walk process and the random transposition or interchange process have the same spectral gap we prove the conjecture using a recursive strategy the approach is a natural extension of the method already used to prove the validity of the conjecture on trees the novelty is an idea based on electric network reduction which reduces the problem to the proof of an explicit inequality for a random transposition operator involving both positive and negative rates the proof of the latter inequality uses suitable coset decompositions of the associated matrices with rows and columns indexed by permutations

schauder a priori estimates and regularity of solutions to boundary degenerate elliptic linear second order partial differential equations abstract we establish schauder a priori estimates and regularity for solutions to a class of boundary degenerate elliptic linear second order partial differential equations furthermore given a c smooth source function we prove c regularity of solutions up to the portion of the boundary where the operator is degenerate boundary degenerate elliptic operators of the kind described in our article appear in a diverse range of applications including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance 10 25 generators of diffusion processes arising in mathematical biology 3 11 and the study of porous media 7 8

2 solvability of the dirichlet problem for nondivergence elliptic equations with vmo coefficients we prove a well posedness result in the class w 2 p w 0 1 p for the dirichlet problem lu f a e in u 0 on we assume the coefficients of the elliptic nondivergence form equation that we study are in vmo l

a low temperature expansion for classical n vector models ii renormalization group equations this paper continues the analysis of the low temperature expansions for classicaln vector models started in 1 a main part of it is a derivation of renormalization group equations and a construction of their solutions to do this we have to introduce a fluctuation integral connected with a next renormalization transformation and to make its preliminary analysis the results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites or actions described inductively in 1

global estimates for quasilinear elliptic equations on reifenberg flat domains new global regularity estimates are obtained for solutions to a class of quasilinear elliptic boundary value problems the coefficients are assumed to have small bmo seminorms and the boundary of the domain is sufficiently flat in the sense of reifenberg the main regularity estimates obtained are in weighted lorentz spaces other regularity results in lorentz morrey morrey and holder spaces are shown to follow from the main estimates

parabolic equations in reifenberg domains natural sobolev type estimates are proved for weak solutions of inhomogeneous parabolic equations in divergence form in a bounded cylinder 0 t which is reifenberg flat in the space direction the principal coefficients of the operator are assumed to be in bmo space with their bmo semi norms small enough

exponential dichotomy on the real line svd and qr methods abstract in this work we show when and how techniques based on the singular value decomposition svd and the qr decomposition of a fundamental matrix solution can be used to infer if a system enjoys or not exponential dichotomy on the whole real line

robustness for impulsive equations for nonautonomous linear impulsive differential equations in banach spaces we establish the robustness of exponential contractions and exponential dichotomies in the sense that the exponential behavior persists under sufficiently small linear perturbations we also consider the more general case of nonuniform exponential behavior