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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：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：Jagannath, Aukosh; Lopatto, Patrick; Miolane, Leo
作者单位：Harvard University; University of Waterloo; University of Waterloo; Inria; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same. Furthermore, we find that the maximum likelihood estimator achieves the maximal correlation with the planted vector among measurable estimators above the estimation threshold. In this setting, the maximum likelihood estimator exhibits a discontinuous BBP-type...
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作者：Briand, Philippe; De Raynal, Paul-Eric Chaudru; Guillin, Arnaud; Labart, Celine
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on its law. These reflected equations have been introduced recently in a backward form by Briand, Elie and Hu (Ann. Appl. Probab. 28 (2018) 482-510) in the context of risk measures. We here focus on the forward version of such reflected equations. Our main objective is to provide an approximation of the solutions with the help of interacting particl...
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作者：Nutz, Marcel; Zhang, Yuchong
作者单位：Columbia University; Columbia University; University of Toronto
摘要：Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time of stopping, or a company may condition on not being bankrupt. We observe that conditional optimization is time-inconsistent due to the dynamic change of the conditioning probabi...
