3-4期

最新文章

• High order correctors and two-scale expansions in stochastic homogenization AI翻译
  作者：Gu, Yu
  作者单位：Stanford University
  摘要：In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on , with the random coefficients constructed from i.i.d. random variables. We prove moment bounds on the high order correctors and their gradients under dimensional constraints. It implies the existence of stationary correctors and stationary gradients in high dimensions. As an application, we prove a two-scale expansion of the solutions to the random PDE, which identi...
• Local microscopic behavior for 2D Coulomb gases AI翻译
  作者：Leble, Thomas
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
  摘要：The study of two-dimensional Coulomb gases lies at the interface of statistical physics and non-Hermitian random matrix theory. In this paper we give a large deviation principle (LDP) for the empirical fields obtained, under the canonical Gibbs measure, by zooming around a point in the bulk of the equilibrium measure, up to the finest averaging scale . The rate function is given by the sum of the renormalized energy of Serfaty et al. weighted by the inverse temperature, and of the specific rel...
• Random-cluster dynamics in Z2 AI翻译
  作者：Blanca, Antonio; Sinclair, Alistair
  作者单位：University of California System; University of California Berkeley
  摘要：The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the random-cluster model in the canonical case where the underlying graph is an box in the Cartesian lattice . Our main result is a upper bound for the mixing time at all values of the model parameter p except the critical point , and for all values of the second...
• Exchangeable graph-valued Feller processes AI翻译
  作者：Crane, Harry
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：The transition law of every exchangeable Feller process on the space of countable graphs is determined by a -finite measure on the space of -valued arrays. In discrete time, this characterization gives rise to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous time, the behavior is enriched by a L,vy-It-Khintchine-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-...
• Sufficient conditions for the filtration of a stationary processes to be standard AI翻译
  作者：Ceillier, Gael; Leuridan, Christophe
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
  摘要：Let X be a stationary process with values in some -finite measured state space , indexed by . Call its natural filtration. In Ceillier (Ann Probab 40(5):1980-2007, 2012), sufficient conditions were given for to be standard when E is finite, and the proof used a coupling of all probabilities on the finite set E. In this paper, we construct a coupling of all laws having a density with regard to , which is much more involved. Then, we provide sufficient conditions for to be standard, generalizing...
• Conditioned limit theorems for products of random matrices AI翻译
  作者：Grama, Ion; Le Page, Emile; Peigne, Marc
  摘要：Let g1, g2,... be i. i. d. random matrices in GL (d, R). For any n >= 1 consider the product G(n) = g(n) ... g(1) and the random process G(n)v = g(n) ... g(1)v in R-d starting at point v is an element of R-d \ {0}. It is well known that under appropriate assumptions, the sequence (log ||G(n)v||) (n >= 1) behaves like a sum of i. i. d. r. v.' s and satisfies standard classical properties such as the law of large numbers, the law of iterated logarithm and the central limit theorem. For any vecto...
• On aggregation for heavy-tailed classes AI翻译
  作者：Mendelson, Shahar
  作者单位：Technion Israel Institute of Technology
  摘要：We introduce an alternative to the notion of 'fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot always be attained by a learning procedure (i.e., a procedure that selects a function in the given class), we introduce an aggregation procedure that attains that rate under rather minimal assumptions-for example, that the and norms are equivalent on the linear...