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作者：Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Jilin University; University System of Georgia; Georgia Institute of Technology
摘要：We consider a Fokker-Planck equation in a general domain in R-n with L-loc(p) drift term and W-loc(1,p) diffusion term for any p > n. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit be...
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作者：Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin
作者单位：University of Bonn; Technical University of Berlin
摘要：We study a continuous time random walk, X, on Z(d) in an environment of random conductances taking values in (0, infinity). We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for X under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser's iteration scheme.
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作者：Chen, Zhen-Qing; Croydon, David A.; Kumagai, Takashi
作者单位：University of Washington; University of Washington Seattle; University of Warwick; Kyoto University
摘要：Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk on a supercritical percolation cluster or among random conductances bounded uniformly from below in a half-space, quarter-space, etc., converges when rescaled diffusively to a reflecting Brownian motion, which has been one of the important open problems in ...
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作者：Georgii, Hans-Otto; Schreiber, Tomasz; Thaele, Christoph
作者单位：University of Munich; Nicolaus Copernicus University; Ruhr University Bochum
摘要：A branching random tessellation (BRT) is a stochastic process that transforms a coarse initial tessellation of R-d into a finer tessellation by means of random cell divisions in continuous time. This concept generalises the so-called STIT tessellations, for which all cells split up independently of each other. Here, we allow the cells to interact, in that the division rule for each cell may depend on the structure of the surrounding tessellation. Moreover, we consider coloured tessellations, f...
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作者：Lam, Thomas
作者单位：University of Michigan System; University of Michigan
摘要：Let W be a finite Weyl group and (W) over cap be the corresponding affine Weyl group. We show that a large element in (W) over cap, randomly generated by (reduced) multiplication by simple generators, almost surely has one of vertical bar W vertical bar-specific shapes. Equivalently, a reduced random walk in the regions of the affine Coxeter arrangement asymptotically approaches one of vertical bar W vertical bar-many directions. The coordinates of this direction, together with the probabiliti...
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作者：Kargin, V.
作者单位：University of Cambridge
摘要：This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. I...
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作者：Ahlberg, Daniel
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart-the Hsu-Robbins-Erdos ...
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作者：Dalang, Robert C.; Mueller, Carl
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester
摘要：It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases where (k - 1)d = 2kN, there are a.s. no k-multiple points.
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作者：Gravner, Janko; Holroyd, Alexander E.
作者单位：University of California System; University of California Davis; Microsoft
摘要：We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random initial seed on an interval of length L, with probability tending to one as L -> infinity, the evolution is a replicator. That is, a region of space time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of oth...
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作者：Neininger, Ralph; Sulzbach, Henning
作者单位：Goethe University Frankfurt
摘要：Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to the space C[0, 1] of continuous functions endowed with uniform topology and the space D[0, 1] of cadlag functions with the Skorokhod topology. The contraction method originated from the probabilistic analysis of algorithms and random trees where characterist...
