-
作者：Huo, Ran; Durrett, Rick
作者单位：Duke University
摘要：Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if x has degree d(x) then at rate d(x)p(k) the individual at x consults k >= 1 neighbors. If at least one neighbor is 1, they adopt...
-
作者：Reinert, Gesine; Ross, Nathan
作者单位：University of Oxford; University of Melbourne
摘要：We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in high temperature regimes.
-
作者：Heydecker, Daniel
作者单位：University of Cambridge
摘要：We derive two estimates for the deviation of the N-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our estimates, exploiting the stability properties of the limiting Boltzmann equation at the level of realisations of the interacting particle system. As a consequence, we obtain an estimate for the propagation of chaos, uniformly in time and with polynomial rates, as so...
-
作者：Leobacher, Gunther; Szoelgyenyi, Michaela
作者单位：University of Graz; University of Klagenfurt
-
作者：Jaber, Eduardo Abi; Larsson, Martin; Pulido, Sergio
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Federal Institutes of Technology Domain; ETH Zurich; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier-Laplace functional in terms of the solution of an associated system of deterministic integral equations of convolution type, extending well-known form...
-
作者：Diehl, Christina S.; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：We study tree lengths in Lambda-coalescents without a dust component from a sample of n individuals. For the total length of all branches and the total length of all external branches, we present laws of large numbers in full generality. The other results treat regularly varying coalescents with exponent 1, which cover the Bolthausen-Sznitman coalescent. The theorems contain laws of large numbers for the total length of all internal branches and of internal branches of order a (i.e., branches ...
-
作者：Gorham, Jackson; Duncan, Andrew B.; Vollmer, Sebastian J.; Mackey, Lester
作者单位：Stanford University; Imperial College London; University of Warwick; Microsoft
摘要：Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targets have been analyzed. We introduce a new class of characterizing operators based on Ito diffusions and develop explicit multivariate Stein factor bounds for any target with a f...
-
作者：Sankararaman, Abishek; Baccelli, Francois; Foss, Sergey
作者单位：University of Texas System; University of Texas Austin; Heriot Watt University; Novosibirsk State University; Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Consider a countably infinite collection of interacting queues, with a queue located at each point of the d-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the processor sharing type, with the service rate in each queue slowed down, when the neighboring queues have a larger workload. The interactions are translation invariant in space and is neither of the Jackson Networks type, nor of the mean-field type. Coupling and pe...
