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作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erdos-Renyi random graph G(n, d/n), where each edge is chosen independently with probability d/n and d is fixed. While the average degree in G(n, d/n) is d(1-o(1)), it contains many nodes of degree of order (log n)/(log log n). The existence of nodes of almost logarithmic degrees implies that for many na...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：The polynomial ergodic theorem ( PET) which appeared in Bergelson (Ergod. Th. Dynam. Sys. 7, 337-349, 1987) and attracted substantial attention in ergodic theory studies the limits of expressions having the form 1/N Sigma(N)(n=1) T-q1(n) f(1) ... T-ql(n) f(l) where T is a weakly mixing measure preserving transformation, f(i)'s are bounded measurable functions and q(i)'s are polynomials taking on integer values on the integers. Motivated partially by this result we obtain a central limit theore...
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作者：Mariani, Mauro
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. A second order large deviations principle is therefore investigated, however, this can ...
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作者：Cheliotis, Dimitris; Virag, Balint
作者单位：Eindhoven University of Technology; University of Toronto
摘要：We consider random walk on a mildly random environment on finite transitive d-regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.
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作者：Driver, Bruce K.; Gordina, Maria
作者单位：University of California System; University of California San Diego; University of Connecticut
摘要：We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure mu on these groups are studied. In particular, we establish a unitary equivalence between the square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the Lie algebra of this class of groups. Using quasi-invariance of the...
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作者：Freidlin, M.; Koralov, L.
作者单位：University System of Maryland; University of Maryland College Park
摘要：In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.
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作者：van der Hofstad, Remco; Luczak, Malwina J.
作者单位：University of London; London School Economics & Political Science; Eindhoven University of Technology
摘要：We study random subgraphs of the 2-dimensional Hamming graph H(2, n), which is the Cartesian product of two complete graphs on n vertices. Let p be the edge probability, and write p = (1 + epsilon)/(2(n - 1)) for some epsilon is an element of R. In Borgs et al. (Random Struct Alg 27:137-184, 2005; Ann Probab 33:1886-1944, 2005), the size of the largest connected component was estimated precisely for a large class of graphs including H(2, n) for e <= Lambda V-1/3, where Lambda > 0 is a constant...
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作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：Seoul National University (SNU); Seoul National University (SNU); University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we study the precise behavior of the transition density functions of censored (resurrected) alpha-stable-like processes in C-1,C-1 open sets in R-d, where d >= 1 and alpha is an element of (1, 2). We first show that the semigroup of the censored alpha-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored alpha-stable-like processes in C...
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作者：Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
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作者：Boutillier, Cedric; de Tiliere, Beatrice
作者单位：Universite Paris Cite; Sorbonne Universite; University of Neuchatel
摘要：We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical Z(2), triangular and honeycomb lattice at the critical temperature. Fisher (J Math Phys 7: 1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dim...
