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作者：Chayes, L; Swindle, G
作者单位：University of California System; University of California Santa Barbara
摘要：We analyze a new class of one-dimensional interacting particle systems featuring random boundaries with a random motion that is coupled to the local particle density. We show that the hydrodynamic limiting behavior in these systems corresponds to the solution of an appropriate Stefan (free-boundary) equation and describe some applications of these results.
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作者：Landim, C; Olla, S; Yau, HT
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; New York University
摘要：The hydrodynamical limit of asymmetric simple exclusion processes is given by an inviscid Burgers equation and its next-order correction is given by the viscous Burgers equation. The diffusivity can be characterized by an abstract formulation in a Hilbert space with the inverse of the diffusivity characterized by a variational formula. Alternatively, it can be described by the Green-Kubo formula. We give arguments that these two formulations are equivalent. We also derive two other variational...
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作者：Sznitman, AS
摘要：We associate certain translation invariant random metrics on R(d) to Brownian motion evolving in a truncated Poissonian potential. These metrics behave over large distances, in an appropriate sense, like certain deterministic norms (the so-called Lyapounov exponents). We prove here upper bounds on the size of fluctuations of the metrics around their mean. Under an additional assumption of rotational invariance, we also derive upper bounds on the difference between the mean of the metrics and t...
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作者：Albin, JMP
作者单位：University of Gothenburg
摘要：We study low local extremes of Gaussian random fields with values in a separable Hilbert space and constant variance. Our results are sharp for certain stationary processes on the line and for these processes we also prove global limits.
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作者：Mytnik, L
摘要：We study the limiting behavior of large branching particle systems undergoing random motion, whose branching mechanism is affected by a random environment. The weak convergence result is established for a sequence of such particle systems and the limiting process is characterized as the unique solution of a martingale problem. The proof of uniqueness of the solution for the martingale problem requires an extension of standard duality techniques.
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作者：Talagrand, M
作者单位：Sorbonne Universite
摘要：Majorizing measures provide bounds for the supremum of stochastic processes. They represent the most general possible form of the chaining argument going back to Kolmogorov. Majorizing measures arose from the theory of Gaussian processes, but they now have applications far beyond this setting. The fundamental question is the construction of these measures. This paper focuses on the tools that have been developed for this purpose and, in particular, the use of geometric ideas. Applications are ...
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作者：Antal, P; Pisztora, A
作者单位：Harvard University
摘要：We prove large deviation estimates at the correct order for the graph distance of two sites lying in the same cluster of an independent percolation process. We improve earlier results of Gartner and Molchanov and Grimmett and Marstrand and answer affirmatively a conjecture of Kozlov.
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作者：Dalang, RC; Mountford, T
作者单位：University of California System; University of California Los Angeles
摘要：For a Brownian sheet on the nonnegative quadrant, we show that any nontrivial curve in the quadrant with the property that the Brownian sheet restricted to the curve gives rise to a differentiable function cannot be differentiable at any point. This result has several implications for level sets of the Brownian sheet. In particular, any Jordan are contained in a level set must be nowhere differentiable.
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作者：Thorisson, H
摘要：Consider a locally compact second countable topological transformation group acting measurably on an arbitrary space. We show that the distributions of two random elements X and X' in this space agree on invariant sets if and only if there is a random transformation Gamma such that Gamma X has the same distribution as X'. Applying this to random fields in d dimensions under site shifts, we show further that these equivalent claims are also equivalent to site-average total variation convergence...
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作者：Aspandilarov, S; Iasnogorodski, R; Menshikov, M
作者单位：Universite de Orleans; Lomonosov Moscow State University
摘要：In this paper we get some sufficient conditions for the finiteness or nonfiniteness of the passage-time moments for nonnegative discrete parameter processes. The developed criteria are closely connected with the well-known results of Foster for the ergodicity of Markov chains and are given in terms of sub(super)martingales. Then, as an application of the obtained results, we get explicit conditions for the finiteness or nonfiniteness of passage-time moments for reflected random walks in a quad...
