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作者：Motte, Mederic; Huyen Pham
作者单位：Universite Paris Cite
摘要：We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such model, called CMKV-MDP for conditional McKean- Vlasov MDP, arises and is obtained here rigorously with a rate of convergence as the asymptotic problem of N-cooperative agents controlled by a social planner/influencer that observes the environment noises but no...
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作者：Olesker-Taylor, Sam
作者单位：University of Bath
摘要：Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate lambda and depart at rate 1. If a call arrives to a link xy, connecting stations x and y, which is at capacity, then a third station z is chosen uniformly at random and the call is attempted to be routed via z: if both links xz and zy have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this ...
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作者：Bufetov, Alexey; Gorin, Vadim; Romik, Dan
作者单位：Leipzig University; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Davis
摘要：The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multispecies version of the totally asymmetric simple exclusion process (TASEP) on a finite interval. An open problem from a 2009 paper of Angel, Holroyd, and Romik asks for the limiting distribution of the absorbing time of the process as the number of particles goes to infinity. We resolve this question by proving that this random variable satisfies GOE Tracy-Widom asymptotics. As ...
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作者：Forien, Raphael; Pardoux, Etienne
作者单位：INRAE; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：This paper presents a new view of household epidemic models, where we exploit the fact that the interaction between the households is of mean field type. We prove the convergence, as the number of households tends to infinity, of the number of infectious individuals in a uniformly chosen household to a nonlinear Markov process solving a McKean-Vlasov Poisson driven stochastic differential equation, as well as a propagation of chaos result. We also define a basic reproduction number R-* and sho...
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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：Bernou, Armand; Fournier, Nicolas
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87-107) and (Comm. Math. Phys. 318 (2013) 375-409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension...
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作者：Beffara, Vincent; Chhita, Sunil; Johansson, Kurt
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Royal Institute of Technology
摘要：Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture...
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作者：Han, Qiyang; Kato, Kengo
作者单位：Rutgers University System; Rutgers University New Brunswick; Cornell University
摘要：A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the distributional limit in many nonregular statistical estimation problems, the accuracy of Chernoff-type approximations has remained largely unknown. In the present paper, we tackle this problem and derive Berry-Esseen bounds for Chernoff-type limit distributions i...
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作者：Blanca, Antonio; Caputo, Pietro; Parisi, Daniel; Sinclair, Alistair; Vigoda, Eric
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Roma Tre University; University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice Z(d). This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is nonlocal, that is, it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any n-vertex cube in Z(d) is O (log n), and we prove this is tight by establishing a matching lower bound on the mixing time...
