-
作者：Chang, Yinshan; Sapozhnikov, Artem
作者单位：Max Planck Society
摘要：We are interested in the clusters formed by a Poisson ensemble of Markovian loops on infinite graphs. This model was introduced and studied in Le Jan (C R Math Acad Sci Paris 350(13-14):643-646, 2012, Ill J Math 57(2):525-558, 2013). It is a model with long range correlations with two parameters and . The non-negative parameter measures the amount of loops, and plays the role of killing on vertices penalizing () or favoring () appearance of large loops. It was shown in Le Jan (Ill J Math 57(2)...
-
作者：Corwin, Ivan; Hammond, Alan
作者单位：Columbia University; Sorbonne Universite; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：For each t >= 1we construct an -indexed ensemble of random continuous curves with three properties: the lowest indexed curve is distributed as the time t Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation with narrow wedge initial data; the entire ensemble satisfies a resampling invariance which we call the -Brownian Gibbs property [with H(x) = e(x)]; increments of the lowest indexed curve, when centered by and scaled down vertically by and horizontall...
-
作者：Teixeira, Augusto
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper we establish some relations between percolation on a given graph G and its geometry. Our main result shows that, if G has polynomial growth and satisfies what we call the local isoperimetric inequality of dimension , then . This gives a partial answer to a question of Benjamini and Schramm (Electron Commun Probab 1(8):71-82 1996). As a consequence of this result and Haggstrom (Adv Appl Probab 32(1):39-66 2000) we derive, that these graphs also undergo a non-trivial phase transiti...
-
作者：Iyer, Gautam; Novikov, Alexei
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on intermediate time scales before diffusion sets in. Various heuristics suggest that an anomalous diffusive behaviour should be observed. We prove that the variance on intermediate time scales grows like . Hence, on these time scales the effective behaviour can not be purely diffusive, and is consistent with an anom...
-
作者：Dias, J. C. A.; Friedli, S.
作者单位：Universidade Federal de Minas Gerais
摘要：We take a closer look at a class of chains with complete connections introduced by Berger, Hoffman and Sidoravicius. In particular, besides giving a sharper description of the uniqueness and non-uniqueness regimes, we show that if the pure majority rule used to fix the dependence on the past is replaced with a function that is Lipschitz at the origin, then uniqueness always holds, even with arbitrarily slow decaying variation.
-
作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：Any renewal processes on N-0 with a polynomial tail, with exponent a is an element of (0, 1), has a non-trivial scaling limit, known as the alpha-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i. i. d. random environment, called disordered pinning models. We show that for alpha is an element of (1/2, 1) these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subse...
-
作者：Tsai, Li-Cheng
作者单位：Stanford University
摘要：In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion, for all . Our construction applies to an explicit and general class of initial conditions, including the lattice configuration and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (...
-
作者：Curien, Nicolas; Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We study the random metric space called the Brownian plane, which is closely related to the Brownian map and is conjectured to be the universal scaling limit of many discrete random lattices such as the uniform infinite planar triangulation. We obtain a number of explicit distributions for the Brownian plane. In particular, we consider, for every , the hull of radius r, which is obtained by filling in the holes in the ball of radius r centered at the root. We introduce a quantity which is inte...
-
作者：Chazottes, J. -R.; Collet, P.; Meleard, S.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study a general class of birth-and-death processes with state space N that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is measured in terms of a 'carrying capacity' K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct. Our aim is to quantify the behavior of the process and the mean time to extinction in the q...
-
作者：Bernardin, Cedric; Goncalves, Patricia; Sethuraman, Sunder
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Universidade do Minho; University of Arizona
摘要：With respect to a class of long-range exclusion processes on , with single particle transition rates of order , starting under Bernoulli invariant measure with density , we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on , d and with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the sc...
