Probability Theory and Related Fields

最新文章

• Critical Brownian multiplicative chaos AI翻译
  作者：Jego, Antoine
  作者单位：University of Vienna
  摘要：Brownian multiplicative chaos measures, introduced in Jego (Ann Probab 48:15971643, 2020), Aidekon et al. (Ann Probab 48(4):1785-1825, 2020) and Bass et al. (Ann Probab 22:566-625, 1994), are random Borel measures that can be formally defined by exponentiating. times the square root of the local times of planar Brownian motion. So far, only the subcritical measures where the parameter gamma is less than 2 were studied. This article considers the critical case where gamma = 2, using three diffe...
• Does a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space? AI翻译
  作者：Herold, Felix; Hug, Daniel; Thale, Christoph
  作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Ruhr University Bochum
  摘要：Poisson processes in the space of (d - 1)-dimensional totally geodesic subspaces (hyperplanes) in a d-dimensional hyperbolic space of constant curvature -1 are studied. The k-dimensional Hausdorff measure of their k-skeleton is considered. Explicit formulas for first- and second-order quantities restricted to bounded observation windows are obtained. The central limit problem for the k-dimensional Hausdorff measure of the k-skeleton is approached in two different set-ups: (i) for a fixed windo...
• A planar Ising model of self-organized criticality AI翻译
  作者：Forien, Nicolas
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finite-size scaling results of Cerf and Messikh (Theory Relat Fields 150(1-2):193-217, 2011. ), we show that, when the size of the box grows to infinity, the temperature concentrates around the critical temperature of...
• Publications of Harry Kesten AI翻译
  作者：Kesten, Harry
• N-sided radial Schramm-Loewner evolution AI翻译
  作者：Healey, Vivian Olsiewski; Lawler, Gregory F.
  作者单位：University of Chicago; Texas State University System; Texas State University San Marcos
  摘要：We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of n-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on n-tuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been conside...
• Near-critical 2D percolation with heavy-tailed impurities, forest fires and frozen percolation AI翻译
  作者：van den Berg, Jacob; Nolin, Pierre
  作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam; City University of Hong Kong
  摘要：We introduce a new percolation model on planar lattices. First, impurities (holes) are removed independently from the lattice. On the remaining part, we then consider site percolation with some parameter p close to the critical value p(c). The mentioned impurities are not only microscopic, but allowed to be mesoscopic (heavy-tailed, in some sense). For technical reasons (the proofs of our results use quite precise bounds on critical exponents in Bernoulli percolation), our study focuses on the...
• Diffusions interacting through a random matrix: universality via stochastic Taylor expansion AI翻译
  作者：Dembo, Amir; Gheissari, Reza
  作者单位：Stanford University; Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：Consider (X-i (t)) solving a system of N stochastic differential equations interacting through a random matrix J = (J(ij)) with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of (X-i (t)), initialized from some mu independent of J, are universal, i.e., only depend on the choice of the distribution J through its first and second moments (assuming e.g., sub-exponential tails). We take a general combinatorial approa...
• Motion by mean curvature in interacting particle systems AI翻译
  作者：Huang, Xiangying; Durrett, Rick
  作者单位：University of British Columbia; Duke University
  摘要：There are a number of situations in which rescaled interacting particle systems have been shown to converge to a reaction diffusion equation (RDE) with a bistable reaction term, see e.g., Cox et al. (Asterisque 349:1-127, 2013), Durrett (Ann Appl Prob 19:477-496, 2009, Electron J Probab 19:1-64, 2014), Durrett and Neuhauser (Ann Probab 22:289-333, 1994). These RDEs have traveling wave solutions. When the speed of the wave is nonzero, block constructions have been used to prove the existence or...
• How linear reinforcement affects Donsker's theorem for empirical processes (vol 178, pg 1173, 2020) AI翻译
  作者：Bertoin, Jean
  作者单位：University of Zurich
• Fluctuations of extreme eigenvalues of sparse Erdos-Renyi graphs AI翻译
  作者：He, Yukun; Knowles, Antti
  作者单位：University of Zurich; University of Geneva
  摘要：We consider a class of sparse random matrices which includes the adjacency matrix of the Erdos-Renyi graph G(N, p). We show that if N-epsilon <= Np <= N1/3-epsilon then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48:916-962, 2020) on the fluctuations of the extreme eigenvalues from Np ...