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作者：Faggionato, A.; Jara, M.; Landim, C.
作者单位：Sapienza University Rome; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a system of particles performing nearest neighbor random walks on the lattice Z under hard-core interaction. The rate for a jump over a given bond is direction-independent and the inverse of the jump rates are i.i.d. random variables belonging to the domain of attraction of an alpha-stable law, 0 < alpha < 1. This exclusion process models conduction in strongly disordered 1D media. We prove that, when varying over the disorder and for a suitable slowly varying function L, under the su...
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作者：Ambrosio, Luigi; Savare, Giuseppe; Zambotti, Lorenzo
作者单位：Universite Paris Cite; Sorbonne Universite; Scuola Normale Superiore di Pisa; University of Pavia
摘要：We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition probabilities. The main result is the following stability property: if the associated invariant measures converge weakly, then the Markov processes converge in law. The proofs are based on the interpretation of a Fokker-Planck equation as the steepest desce...
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作者：Peche, Sandrine
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：For sample covariance matrices with i.i.d. entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches one, it is a well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples. In this paper, we extend this result to two cases. The first case is when the ratio approaches an arbitrary finite value. The second case is when the ratio becomes infinite or arbitrarily s...
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作者：Khoshnevisan, Davar; Xiao, Yimin
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：Let X-1 , . . . , X-N denote N independent d-dimensional Levy processes, and consider the N-parameter random field (sic)(t) := X-1(t(1))+ . . . + X-N (t(N)). First we demonstrate that for all nonrandom Borel sets F subset of R-d, the Minkowski sum (sic)(R-+(N)) circle plus F, of the range (sic)(R-+(N)) of (sic) with F, can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earlier joint effort with Yuquan Zhong by removing a certa...
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作者：Mossel, Elchanan; Weitz, Dror; Wormald, Nicholas
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Waterloo
摘要：We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity lambda, where the weight of an independent set I is lambda(|I|). A recent result has established that Gibbs sampling is rapidly mixing in sampling the distribution for graphs of maximum degree d and lambda < lambda (c) (d), where lambda (c) (d) is the critical activity for uniqueness of the Gibbs measure (i.e., for decay of correlations with distance in the weight...
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作者：Buraczewski, Dariusz; Damek, Ewa; Guivarc'h, Yves; Hulanicki, Andrzej; Urban, Roman
作者单位：University of Wroclaw; Universite de Rennes
摘要：We consider a stochastic recursion Xn+1 = Mn+1Xn + Q(n+1), (n is an element of N), where (Q(n), M-n) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space R-d and X-n is an element of R-d. In the present paper we show that if the recursion has a unique stationary measure nu with unbounded support then the weak limit of properly dilated. exists and defines a homogeneous tail measure Lambda. The structure of Lambda is studied and the supports of nu...
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作者：Bolthausen, Erwin; Funaki, Tadahisa; Otobe, Tatsushi
作者单位：University of Tokyo; University of Zurich
摘要：We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of R-d, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the st...
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作者：Durand, Arnaud
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We completely describe the size and large intersection properties of the Holder singularity sets of L,vy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a L,vy process. The Holder singularity sets of the sample paths of certain random wavelet series are investigated as well.
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作者：Jara, M. D.; Landim, C.; Sethuraman, S.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Iowa State University
摘要：We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation.
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13
摘要：We consider a system of d non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional space-time white noise. The non-linearities appear both as additive drift terms and as multipliers of the noise. Using techniques of Malliavin calculus, we establish upper and lower bounds on the one-point density of the solution u(t, x), and upper bounds of Gaussian-type on the two-point density of (u(s, y), u(t, x)). In particular, this estimate quantifies how this density degenerate...
