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作者：Blancas, Airam; Rogers, Tim; Schweinsberg, Jason; Siri-Jegousso, Arno
作者单位：Goethe University Frankfurt; University of Bath; University of California System; University of California San Diego; Universidad Nacional Autonoma de Mexico
摘要：The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time t decays as 2 gamma/ct(2), where c is the ratio of the coalescence rates at the individual and species levels, and t...
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作者：Bion-Nadal, Jocelyne; Talay, Denis
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Inria; Universite Cote d'Azur
摘要：In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton-Jacobi-Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an...
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作者：Van Hao Can
作者单位：Vietnam Academy of Science & Technology (VAST)
摘要：In a recent paper, Giardina et al. [ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016) 121-161] have proved a law of large number and a central limit theorem with respect to the annealed measure for the magnetization of the Ising model on some random graphs, including the random 2-regular graph. In this paper, we present a new proof of their results which applies to all random regular graphs. In addition, we prove the existence of annealed pressure in the case of configuration model random graphs.
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作者：Budhiraja, Amarjit; Mukherjee, Debankur; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; University of Michigan System; University of Michigan
摘要：We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson processes with rate lambda, and each task is irrevocably assigned to the shortest queue among the one it first appears and its d - 1 randomly selected neighbors. This model has been extensively studied when...
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作者：Jin, Ke
作者单位：University of Delaware
摘要：The Mallows measure is a probability measure on S-n where the probability of a permutation pi is proportional to q(l(pi)) with q > 0 being a parameter and l(pi) the number of inversions in pi. We prove a weak law of large numbers for the length of the longest common subsequences of two independent permutations drawn from the Mallows measure, when q is a function of n and n(1 - q) has limit in R as n ->infinity.
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作者：Kloeckner, Benoit
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Applying quantitative perturbation theory for linear operators, we prove nonasymptotic bounds for Markov chains whose transition kernel has a spectral gap in an arbitrary Banach algebra of functions X. The main results are concentration inequalities and Berry-Esseen bounds, obtained assuming neither reversibility nor warm start hypothesis: the law of the first term of the chain can be arbitrary. The spectral gap hypothesis is basically a uniform X - ergodicity hypothesis, and when X consist in...
