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作者：Gravner, Janko; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least. occupied neighbors. The initially occupied set is random, given by a uniform product measure with a low density p. Our main focus is on this process on the product graph Z(2) x K-n(2), where K-n is a complete graph. We investigate how p scales with n so that a typical site is eventually occupied. Under critical scaling, the dynamics with even. exhibit...
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作者：Horton, Emma; Kyprianou, Andreas E.; Villemonais, Denis
作者单位：Universite de Lorraine; University of Bath
摘要：The neutron transport equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatial Markov branching process which describes the process of nuclear fission, transport, scattering, and absorption. By reformulating the NTE in its mild form and identifying its solution as an expectation semigroup, we use modern techniques to develop a Perron-Frobenius (PF) type decomposition, showing that growth is d...
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作者：Carinci, Gioia; Giardina, Cristian; Redig, Frank
作者单位：Delft University of Technology; Universita di Modena e Reggio Emilia
摘要：We consider two particles performing continuous-time nearest neighbor random walk on Z and interacting with each other when they are at neighboring positions. The interaction is either repulsive (partial exclusion process) or attractive (inclusion process). We provide an exact formula for the Laplace-Fourier transform of the transition probabilities of the two-particle dynamics. From this we derive a general scaling limit result, which shows that the possible scaling limits are coalescing Brow...
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作者：Mailler, Cecile; Villemonais, Denis
作者单位：University of Bath; Inria; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a noncompact space. Our motivation is to apply this result to measure-valued Polya processes (MVPPs, also known as infinitely-many Polya urns). Our main idea is to use Foster-Lyapunov type criteria in a novel way to generalize stochastic-approximation methods to measure-valued Markov processes with a noncompact underlying space, overcoming in a fairly general context ...
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作者：Betz, Volker; Schaefer, Helge; Zeindler, Dirk
作者单位：Technical University of Darmstadt; Lancaster University
摘要：We consider uniform random permutations of length n conditioned to have no cycle longer than n(beta) with 0 < beta < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson conver...
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作者：Holden, Nina; Lyons, Russell
作者单位：Massachusetts Institute of Technology (MIT); Indiana University System; Indiana University Bloomington
摘要：In the trace reconstruction problem, an unknown bit string x is an element of {0, 1}(n) is sent through a deletion channel where each bit is deleted independently with some probability q is an element of (0, 1), yielding a contracted string (x) over tilde. How many i.i.d. samples of (x) over tilde are needed to reconstruct x with high probability? We prove that there exist x, y is an element of {0, 1}(n) such that at least cn(5/4)/root log n traces are required to distinguish between x and y f...
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作者：Butkovsky, Oleg; Kulik, Alexei; Scheutzow, Michael
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Wroclaw University of Science & Technology; Technical University of Berlin
摘要：We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtained results to show exponential ergodicity of a variety of nonlinear stochastic partial differential equations with additive forcing, including 2D stochastic Navier-Stokes equations. Our main tool is a new version of the generalized coupling method.
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作者：Mourrat, J-C
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in Mourrat (2018) which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of Mourrat (2018) using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the nonlinearity in the equation is convex.
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作者：Ben-Hamou, Anna
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we are interested in the impact of communities on the mixing behavior of the nonbacktracking random walk. We consider sequences of sparse random graphs of size N generated according to a variant of the classical configuration model which incorporates a two-community structure. The strength of the bottleneck is measured by a parameter alpha which roughly corresponds to the fraction of edges that go from one community to the other. We show that if alpha >> 1/ log N, then the nonba...
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作者：De Angelis, T.; Peskir, G.
作者单位：University of Leeds; University of Manchester
摘要：We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the stopping set, then the boundary point is Green regular for the stopping set. Combining this implication with the existence of a continuously differentiable flow of the process we show that the value function is continuously differentiable at the optimal stopping b...
