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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...
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作者：Fribergh, Alexander; Gantert, Nina; Popov, Serguei
作者单位：University of Munster; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universidade de Sao Paulo
摘要：We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order ...
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作者：Delbaen, Freddy; Tang, Shanjian
作者单位：Fudan University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations in R-p (p is an element of [1, infinity)) and backward stochastic differential equations (BSDEs) in R-p x H-p (p is an element of (1, infinity)) and in R-infinity x (L-infinity) over bar (BMO), with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality plays a crucial role in the development of our theory, which seems to be new. Se...
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作者：Kotelenez, Peter M.; Kurtz, Thomas G.
作者单位：University System of Ohio; Case Western Reserve University; University of Wisconsin System; University of Wisconsin Madison
摘要：A class of quasilinear stochastic partial differential equations (SPDEs), driven by spatially correlated Brownian noise, is shown to become macroscopic (i.e., deterministic), as the length of the correlations tends to 0. The limit is the solution of a quasilinear partial differential equation. The quasilinear SPDEs are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations (SODEs), coupled though a mean-field interaction an...
