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作者：Ben Alaya, Mohamed; Kebaier, Ahmed; Ngo, Thi Bao Tram
作者单位：Universite de Rouen Normandie; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we give a natural extension of the antithetic multilevel Monte Carlo (MLMC) estimator for a multidimensional diffusion introduced by Giles and Szpruch (Ann. Appl. Probab. 24 (2014) 1585-1620) by considering the permutation between m Brownian increments, m >= 2, instead of using two increments as in the original paper. Our aim is to study the asymptotic behavior of the weak errors involved in this new algorithm. Among the obtained results, we prove that the error between on the o...
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作者：Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We consider a class of Gibbs measures defined with respect to increments {omega(t) - omega(s)}(s 0) and unbounded (singular) interactions (including singularities of the form x bar right arrow 1/vertical bar x vertical bar(p) in d >= 3 or x bar right arrow delta(0)(x) in d = 1) attached to the space variables. These assumptions on the interaction seem to be sharp and cover quantum mechanical models like the Nelson model and the polaron problem with ultraviolet cut off (both carrying bounded sp...
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作者：Helmuth, Tyler; Perkins, Will; Petti, Samantha
作者单位：Durham University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Harvard University
摘要：We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three and higher. As the dimension tends to infinity, our improvements are by factors of 2 and 1.7, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and te...
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作者：Kolokoltsov, Vassili N.
作者单位：University of Warwick
摘要：In this paper we are merging the two new branches of game theory: quantum games and mean-field games (MFG). Building a quantum analog of MFGs requires the full reconstruction of its foundations and methodology, because in N-particle quantum evolution particles are not separated in individual dynamics and the key concept of the classical MFG theory, the empirical measure defined as the sum of Dirac masses of the positions of the players, is not applicable in quantum setting. As a preliminary re...
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作者：Cardaliaguet, Pierre; Souganidis, Panagiotis E.
作者单位：Universite PSL; Universite Paris-Dauphine; University of Chicago
摘要：We consider mean field games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the...
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作者：Pang, Guodong; Pardoux, Etienne
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of infection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these m...
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作者：Banerjee, Sayan; Bhamidi, Shankar
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider models of growing random trees {T-f (n) : n >= 1} with model dynamics driven by an attachment function f : Z(+) -> R+. At each stage a new vertex enters the system and connects to a vertex v in the current tree with probability proportional to f (degree(v)). The main goal of this study is to understand the performance of root finding algorithms. A large body of work (e.g., Random Structures Algorithms 50 (2017) 158-172; IEEE Trans. Netw. Sci. Eng. 4 (2017) 1-12; Random Structures A...
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作者：Bai, Tianyi; Wan, Yijun
作者单位：New York University; NYU Shanghai; Universite PSL; Ecole Normale Superieure (ENS)
摘要：By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
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作者：Yasodharan, Sarath; Sundaresan, Rajesh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：This paper studies large deviations of a fully coupled finite state meanfield interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two ...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dewaskar, Miheer
作者单位：University of North Carolina; University of North Carolina Greensboro; Duke University
摘要：We consider the supermarket model in the usual Markovian setting where jobs arrive at rate n.n for some lambda(n) > 0, with n parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest among d(n) <= n randomly selected service queues. We show that when d(n) -> infinity and lambda(n) -> lambda is an element of (0,infinity), under natural conditions on the initial queues, the state occupancy process converges in probability, in a suitable path space, to the ...
