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作者：Lil, Jia; Zhang, Congshan; Liu, Yunxiao
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Holder classes as special cases. The gen...
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作者：Erhard, Dirk; Franco, Tertuliano; da Silva, Diogo S.
作者单位：Universidade Federal da Bahia
摘要：We consider the continuous time symmetric random walk with a slow bond on Z, which rates are equal to 1/2 for all bonds, except for the bond of vertices {-1, 0}, which associated rate is given by alpha n(-beta)/2, where alpha > 0 and beta is an element of [0, infinity] are the parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if beta is an element of [0, infinity), then it converges to the usual Brownian motion. If beta is an elemen...
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作者：Gamarnik, David; Kizildag, Eren C.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In particular, we establish that unless P = #P, there does not exist a polynomial-time algorithm to exactly compute the partition function on average. This is done by showing that if there exists a polynomial time algorithm, which exactly computes the partition functi...
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作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：We consider the convex hull of the perturbed point process comprised of n i.i.d. points, each distributed as the sum of a uniform point on the unit sphere Sd-1 and a uniform point in the d-dimensional ball centered at the origin and of radius n(alpha), alpha is an element of (-infinity,infinity). This model, inspired by the smoothed complexity analysis introduced in computational geometry (J. Comput. Geom. 7 (2016) 101-144; J. ACM 51 (2004) 385-463), is a perturbation of the classical random p...
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作者：Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We continue the investigation of the localization phenomenon for a vertex reinforced random walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive probability, and make some conjecture concerning the almost sure behavior.
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作者：Lucon, Eric; Poquet, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in a large population. Each neuron is represented by its voltage and recovery variables, which are the solution to a FitzHugh-Nagumo system, and interacts with the rest of the population through a mean-field linear coupling, in the presence of noise. The aim of the paper is to study the emergence of collective oscillatory behaviors induced by noise and interaction...
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作者：Chen, Louis H. Y.; Rollin, Adrian; Xia, Aihua
作者单位：National University of Singapore; National University of Singapore; University of Melbourne
摘要：We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of normal approximation to statistics arising from random measures, including stochastic geometry. We illustrate the use of the bound in four examples: completely random measures, excursion random measure of a locally dependent random process, and the total edge len...
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作者：Matoussi, Anis; Possamai, Dylan; Zhou, Chao
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Le Mans Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; National University of Singapore
摘要：The aim of this short note is to fill in a gap in our earlier paper (Ann. Appl. Probab. 23 (2013) 2420-2457) on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper (Stochastic Process. Appl. 124 (2014) 2281-2321). We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions (Li and Peng (2017); Soumana Hima (2017)) in the so-called G-framework.
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作者：Bakhtin, Yuri; Chen, Hong-Bin
作者单位：New York University
摘要：For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.
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作者：Bramson, Maury; Gray, Lawrence F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The majority vote process was one of the first interacting particle systems to be investigated. It can be described briefly as follows. There are two possible opinions at each site of a graph G. At rate 1 - epsilon, the opinion at a site aligns with the majority opinion at its neighboring sites and, at rate epsilon, the opinion at a site is randomized due to noise, where epsilon is an element of [0, 1] is a parameter. Despite the simple dynamics of the majority vote process, its equilibrium be...
