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作者：Basu, Riddhipratim; Sly, Allan
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：In this paper, we examine a variant of the voter model on a dynamically changing network where agents have the option of changing their friends rather than changing their opinions. We analyse, in the context of dense random graphs, two models considered in Durrett et al. [Proc. Natl. Acad. Sci. USA 109 (2012) 3682-3687]. When an edge with two agents holding different opinion is updated, with probability &, one agent performs a voter model step and changes its opinion to copy the other, and wit...
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作者：Buckdahn, Rainer; Li, Juan; Ma, Jin
作者单位：Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Shandong University; Shandong University; University of Southern California
摘要：In this paper, we are interested in a new type of mean-field, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths of the state, but also on the conditional law of the state, given the observation to date. Our problem is strongly motivated by the recent study of the mean field games and the related McKean-Vlasov stochastic control problem, but with added aspects of path-depen...
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作者：Watanabe, Shun; Hayashi, Masahito
作者单位：Tokyo University of Agriculture & Technology; Nagoya University; National University of Singapore
摘要：Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean for the Markov chain with finite state space. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the type-2 error under the exponential constraint for the error probability of the type-1 error in a simple hypothesis testing for a finite-length Markov chain, which yields the Hoeffding-type bound. For these derivations, we derive upper...
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作者：Arguin, Louis-Pierre; Belius, David; Harper, Adam J.
作者单位：Universite de Montreal; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; New York University
摘要：A recent conjecture of Fyodorov-Hiary-Keating states that the maximum of the absolute value of the Riemann zeta function on a typical bounded interval of the critical line is exp{loglogT - 3/4logloglogT + O(1)}, for an interval at (large) height T. In this paper, we verify the first two terms in the exponential for a model of the zeta function, which is essentially a randomized Euler product. The critical element of the proof is the identification of an approximate tree structure, present also...
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作者：Ball, Frank; Brittont, Tom; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size n. A Markovian SIR (susceptible -> infective -> recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where n -> infinity, keeping the basic reproduction number R-0 as well as the importation rate of infectives fixed, but assuming that the quotient of the avera...
