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作者：Zheng, Xinghua; Zhu, Qingsan
作者单位：Hong Kong University of Science & Technology; Hong Kong University of Science & Technology
摘要：We study supercritical spatial SIR epidemics on Z2 2 x { 1 , 2 ,.. .,N } , where each site in Z2 2 represents a village and N stands for the village size. We establish several asymptotic results as N-* oc . In particular, we derive the probability that the epidemic will last forever if the epidemic is started by one infected individual.E Moreover, we show that, conditional on that the epidemic lasts forever, the epidemic spreads out linearly in all directions and derive an explicit formula for...
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作者：Baccelli, Francois; Haji-Mrsadeghi, Mir -Omid; Haniha, Sayeh k
作者单位：Inria; Sharif University of Technology
摘要：The Doeblin graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its bridge Doeblin subgraph only contains the paths starting from a tagged point of the state space at all possible times. In the irreducible, aperiodic, and positive recurrent case, the following results are known: the bridge Doeblin g...
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作者：Bensoussan, Alain; Graber, P. Jameson; Yam, Sheung Chi Phillip
作者单位：University of Texas System; University of Texas Dallas; Baylor University; Chinese University of Hong Kong
摘要：We propose a new approach to studying classical solutions of the second order Bellman equation and master equation for mean field type control problems, using a novel form of the lifting idea introduced by P.-L. Lions. Rather than studying the usual system of Hamilton-Jacobi/Fokker-Planck PDEs using analytic techniques, we instead study a stochastic control problem on a specially constructed Hilbert space, which is reminiscent of a tangent space on the Wasserstein space in optimal transport. O...
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作者：Poisat, Julien; Simenhaus, Francois
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the large-time asymptotics of the quenched survival probability. In the present work we continue our study by describing the behaviour of the random walk conditioned to survive. We prove that with large probability, the walk quickly reaches a unique time-dependent optima...
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作者：Amarnik, David; Adik, Ilias
作者单位：Massachusetts Institute of Technology (MIT); New York University
摘要：We study the computational-statistical gap of the planted clique problem, where a clique of size k is planted in an Erdos-Renyi graph G(n, 1/2). The goal is to recover the planted clique vertices by observing the graph. It is known that the clique can be recovered as long as k >= (2 + epsilon) log n for any epsilon > 0, but no polynomial-time algorithm is known for this task unless k = Omega (root n). Following a statistical-physics inspired point of view, as a way to understand the nature of ...
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作者：Ganassali, Luca; Massoulie, Laurent; Semerjian, Guilhem
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Inria; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
摘要：In this paper we address the problem of testing whether two observed trees (t, t') are sampled either independently or from a joint distribution under which they are correlated. This problem, which we refer to as correlation detection in trees, plays a key role in the study of graph alignment for two correlated random graphs. Motivated by graph alignment, we investigate the conditions of existence of one-sided tests, that is, tests which have vanishing type I error and nonvanishing power in th...
