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作者：Ben Arous, Gerard; Cabezas, Manuel; Cerny, Jiri; Royfman, Roman
作者单位：New York University; University of Vienna
摘要：We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on Z. These scaling limits include the well-known fractional kinetics process, the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call spatially subordinated Brownian motions. We give sufficient conditions for convergence and illustrate these on two important examples.
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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：Romik, Dan; Sniady, Piotr
作者单位：University of California System; University of California Davis; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Wroclaw
摘要：We study an infinite version of the jeu de taquin sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson Schensted Knuth (RSK) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variable...
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作者：Viklund, Fredrik Johansson
作者单位：Uppsala University
摘要：We estimate convergence rates for curves generated by Loewner's differential equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is what we call the tip structure modulus, a geometric measure of regularity for Loewner curves parameterized by capacity. It is analogous to Warschawski's boundary structure modulus and closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approachi...
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作者：Le Gall, Jean-Francois; Lin, Shen
作者单位：Universite Paris Saclay
摘要：We study the range R-n, of a random walk on the d-dimensional lattice Z(d) indexed by a random tree with n vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension d <= 3 that n(-d/4)R(n) converges in distribution to the Lebesgue measure of the support of the integrated super-Brownian excursion (ISE). An auxiliary result shows that the suitably rescaled local times of the tree-indexed random walk converge in distribution to the densit...
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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：Ameur, Yacin; Hedenmalm, Haakan; Makarov, Nikolai
作者单位：Lund University; Royal Institute of Technology; California Institute of Technology
摘要：We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the ...
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作者：Fulman, Jason; Goldstein, Larry
作者单位：University of Southern California
摘要：With Q(q,n) the distribution of n minus the rank of a matrix chosen uniformly from the collection of all n x (n + m) matrices over the finite field F-q of size q >= 2, and Q(q) the distributional limit of Q(q,n) as n -> infinity, we apply Stein's method to prove the total variation bound 1/8q(n+m+1) <= parallel to Q(q,n) - Qq parallel to TV <= 3/q(n+m+1). In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew cen...
