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作者：Eichinger, Katharina; Gnann, Manuel V.; Kuehn, Christian
作者单位：Universite PSL; Universite Paris-Dauphine; Delft University of Technology; Technical University of Munich
摘要：We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a scalar stochastic ordinary differential equation (SODE) and tracking perturbations to the wave meeting a system of a scalar stochastic partial differential equation (SPDE) cou...
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作者：McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew B.
作者单位：University of North Carolina; University of North Carolina Charlotte; Duke University; Duke University; Duke University; Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：In this paper we consider the posterior consistency of Bayesian inference procedures when the family of models consists of appropriate stochastic processes. Specifically, we suppose that one observes an unknown ergodic process and one has access to a family of models consisting of dependent processes. In this context, we consider Gibbs posterior inference, which is a loss-based generalization of standard Bayesian inference. Our main results characterize the asymptotic behavior of the Gibbs pos...
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作者：Lachieze-Rey, Raphael; Peccati, Giovanni; Yang, Xiaochuan
作者单位：Universite Paris Cite; University of Luxembourg; Brunel University
摘要：We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the order one-that we evaluate and compare at two different scales-and are specifically tailored for studying the Gaussian fluctuations of sequences of geometric functionals displaying a form of weak stabilization-see Penrose and Yukich (Ann. Appl. Probab. 11 (2001)...
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作者：Bukh, Boris; Cox, Christopher
作者单位：Carnegie Mellon University; Iowa State University
摘要：Let W-(n) be the n-letter word obtained by repeating a fixed word W, and let R-n be a random n-letter word over the same alphabet. We show several results about the length of the longest common subsequence (LCS) between W-(n) and R-n; in particular, we show that its expectation is gamma(W)n - O (root n) for an efficiently-computable constant gamma(W). This is done by relating the problem to a new interacting particle system, which we dub frog dynamics. In this system, the particles (frogs) hop...
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作者：Backhoff-Veraguas, J.; Pammer, G.
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans pi(1), pi(2), ... converges weakly to a transport plan pi, then pi is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain (Ann. Inst. Henri Poincare Probab. Stat. 56 (2020) 1706-1729) asked whether the same property is true for the martingale transport problem. This question seems particularly pressing since martingale transport is motivated by ro...
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作者：Gonzalez Casanova, Adrian; Miro Pina, Veronica; Siri-Jegousse, Arno
作者单位：Universidad Nacional Autonoma de Mexico; Universidad Nacional Autonoma de Mexico
摘要：We define a new class of Xi-coalescents characterized by a possibly infinite measure over the nonnegative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry property on their coagulation rates: they are invariant under any transformation that consists of moving one element from one block to another without changing the total number of blocks. We illustrate the diversity of behaviors of this family of processes by intr...
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作者：Fan, Wai-Tong Louis; Legried, Brandon; ROCH, Sesbastien
作者单位：Indiana University System; Indiana University Bloomington; University of Michigan System; University of Michigan; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed k no statistically consistent phylogeny estimation is possible from k-mer counts over the full leaf sequences alone. Formally, we establish that the joint distribution of k-mer counts over the entire leaf sequences on two distinct trees have total variation distance bounded away from 1 as ...
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作者：Mueller, Carl; Neuman, Eyal
作者单位：University of Rochester; Imperial College London
摘要：We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in (0, infinity). Our main result states that the effective radius of the polymer is approximately J5/3; evidently for large J the polymer undergoes stretching. This contrasts with the equilibrium sit-uation without the time variable, where many earlier results show that the effective radius is approximately J.For such a moving polymer taking values in R2, we offer a conjecture that the eff...
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作者：Lacoin, Hubert; Yang, Shangjie
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study the dynamical behavior of a one dimensional interface interacting with a sticky impenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contacts between the interface and the substrate are given an energetic bonus while an external force with constant intensity pulls the interface away from the wall. Our interface is modeled by the graph of a one-dimensional nearest-neighbor path on Z(+), starting at 0 and ending at 0 after 2N steps, with ...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dewaskar, Miheer
作者单位：University of North Carolina; University of North Carolina Greensboro; Duke University
摘要：We consider the supermarket model in the usual Markovian setting where jobs arrive at rate n.n for some lambda(n) > 0, with n parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest among d(n) <= n randomly selected service queues. We show that when d(n) -> infinity and lambda(n) -> lambda is an element of (0,infinity), under natural conditions on the initial queues, the state occupancy process converges in probability, in a suitable path space, to the ...
