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作者：Banerjee, Sayan; Mukherjee, Debankur
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University System of Georgia; Georgia Institute of Technology
摘要：Consider a system of N parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate.(N). When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (Math. Oper. Res. 43 (2018) 867-886) identified a novel limiting diffusion process that arises as the weak-limit of the appropriately scaled occupancy measure of the syste...
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作者：Garavaglia, Alessandro; van der Hofstad, Remco; Litvak, Nelly
作者单位：Eindhoven University of Technology; University of Twente
摘要：PageRank is a well-known algorithm for measuring centrality in networks. It was originally proposed by Google for ranking pages in the World Wide Web. One of the intriguing empirical properties of PageRank is the so-called 'power-law hypothesis': in a scale-free network, the PageRank scores follow a power law with the same exponent as the (in-)degrees. To date, this hypothesis has been confirmed empirically and in several specific random graphs models. In contrast, this paper does not focus on...
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作者：Benjamini, Itai; Fontes, Luiz Renato; Hermon, Jonathan; Machado, Fabio Prates
作者单位：Weizmann Institute of Science; Universidade de Sao Paulo; University of Cambridge
摘要：We study a system of random walks, known as the frog model, starting from a profile of independent Poisson(lambda) particles per site, with one additional active particle planted at some vertex o of a finite connected simple graph G = (V, E). Initially, only the particles occupying o are active. Active particles perform t is an element of N boolean OR {infinity} steps of the walk they picked before vanishing and activate all inactive particles they hit. This system is often taken as a model fo...
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作者：Blanca, Antonio; Gheissari, Reza; Vigoda, Eric
作者单位：University System of Georgia; Georgia Institute of Technology; New York University
摘要：The random-cluster model with parameters (p, q) is a random graph model that generalizes bond percolation (q = 1) and the Ising and Potts models (q >= 2). We study its Glauber dynamics on n x n boxes Lambda(n) of the integer lattice graph Z(2), where the model exhibits a sharp phase transition at p = p(c)(q). Unlike traditional spin systems like the Ising and Potts models, the random-cluster model has non-local interactions. Long-range interactions can be imposed as external connections in the...
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作者：Dong, Zhao; Wu, Jiang-Lun; Zhang, Rangrang; Zhang, Tusheng
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Swansea University; Beijing Institute of Technology; University of Manchester
摘要：In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.
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作者：Feray, Valentin
作者单位：University of Zurich
摘要：We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeil-berger and Chern, Diaconis, Kane and Rhoades, respectively.
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作者：Mehri, Sima; Scheutzow, Michael; Stannat, Wilhelm; Zangeneh, Ian Z.
作者单位：Technical University of Berlin; Sharif University of Technology
摘要：Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a corresponding propagation of chaos result in the infinite population limit are proven. Our existence result for the McKean-Vlasov equation is based on the Euler approximation that is applied to this type of equation for the first time.
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作者：Nutz, Marcel; San Martin, Jaime; Tan, Xiaowei
作者单位：Columbia University; Columbia University; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n -> infinity. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not lim...
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作者：Gravner, Janko; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least. occupied neighbors. The initially occupied set is random, given by a uniform product measure with a low density p. Our main focus is on this process on the product graph Z(2) x K-n(2), where K-n is a complete graph. We investigate how p scales with n so that a typical site is eventually occupied. Under critical scaling, the dynamics with even. exhibit...
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作者：Butkovsky, Oleg; Kulik, Alexei; Scheutzow, Michael
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Wroclaw University of Science & Technology; Technical University of Berlin
摘要：We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtained results to show exponential ergodicity of a variety of nonlinear stochastic partial differential equations with additive forcing, including 2D stochastic Navier-Stokes equations. Our main tool is a new version of the generalized coupling method.
