-
作者：Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
作者单位：Technion Israel Institute of Technology; Beijing Institute of Technology
摘要：Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.
-
作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model the total occupation measure is known to have a continuously differentiable density (l(x))(x is an element of R), and we write (l(x))(x is an element of R )for its derivative. Although the process (l(x))(x >= 0) is not Markov, we prove that the pair(l(x), l(x))(x >= 0 )is a time-homogeneous Markov proc...
-
作者：Berestycki, Julien; Kim, Yujin h.; Lubetzky, Eyal; Mallein, Bastien; Zeitouni, Ofer
作者单位：University of Oxford; University of Oxford; New York University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a branching Brownian motion in Rd with d >= 1 in which the position X(u) t is an element of Rd of a particle u at time t can be encoded by its direction theta(u) t is an element of Sd-1 and its distance R(u) t to 0. We prove that the extremal point process Sigma delta(theta(u) t,Rt(u)-m(d) t ) (where the sum is over all particles alive at time t and m(d) t is an explicit centering term) converges in distribution to a randomly shifted, decorated Poisson point process on Sd-1 x R. Mo...
-
作者：Bauerschmidt, Roland; Park, Jiwoon; Rodriguez, Pierre-Francois
作者单位：University of Cambridge; Imperial College London
摘要：The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions and at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field. This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As ...
-
作者：Bou-Rabee, Ahmed; Gwynne, Ewain
作者单位：New York University; University of Chicago
摘要：We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is a LQG harmonic ball, which we constructed in a companion paper. We also prove an analogous result for the divisible sandpile.
-
作者：Chapuy, Guillaume; Louf, Baptiste; Walsh, Harriet
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Uppsala University; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of the classical Plancherel measure, which appears naturally in the context of Hurwitz numbers, enumerating certain transposition factorisations in symmetric groups. We study a regime in which the number of factors in the underlying factorisations grows linearl...
-
作者：Gorski, Christian
作者单位：Northwestern University
摘要：We prove a strict monotonicity theorem for first passage percolation on any Cayley graph of a virtually nilpotent group which is not isomorphic to the standard Cayley graph of Z: given two distributions v and v with finite mean, if v is strictly more variable than v and v is subcritical in an appropriate sense, then the expected passage times associated to v exceed those of v by an amount proportional to the graph distance. This generalizes a theorem of van den Berg and Kesten from 1993, which...
-
作者：Tikhomirov, Konstantin; Youssef, Pierre
作者单位：University System of Georgia; Georgia Institute of Technology; New York University; New York University Abu Dhabi
摘要：In this work we develop a comparison procedure for the modified logfinite state space. Efficient comparison of the MLSI Dirichlet forms is a wellknown obstacle in the theory of Markov chains. We approach this problem by introducing a regularized MLSI constant, which, under some assumptions, has the same order of magnitude as the usual MLSI constant yet is amenable for comparison and thus considerably simpler to estimate in certain cases. As an application of this general comparison procedure, ...
-
作者：Andres, Sebastian; Gantert, Nina; Schmid, Dominik; Sous, Perla
作者单位：Braunschweig University of Technology; Technical University of Munich; University of Bonn; University of Cambridge
摘要：We study biased random walks on dynamical percolation on Zd. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for d = 1 the speed is increasing, we show that, in general, this fails in dimension d >= 2. As our main result, we establish two regimes of parameters, separated by an explicit critical curve such t...
-
作者：Casanova, Adrian Gonzalez; Tobias, Andras; Valesin, Daniel
作者单位：Universidad Nacional Autonoma de Mexico; Budapest University of Technology & Economics; University of Warwick
摘要：We introduce and study an interacting particle system evolving on the ddimensional torus (Z/NZ)d. Each vertex of the torus can be either empty or occupied by an individual of type lambda is an element of (0, infinity). An individual of type lambda dies with rate one and gives birth at each neighboring empty position with rate lambda; moreover, when the birth takes place, the newborn individual is likely to have the same type as the parent but has a small probability of being a mutant. A mutant...
