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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massoulie and Roberts [Telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows present in a network. The weighted alpha-fair and weighted max-min fair bandwidth sharing policies are among important policies that have bee...
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作者：Coupier, David
作者单位：Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：A d-dimensional binary Markov random field on a lattice torus is considered. As the size n of the lattice tends to infinity, potentials a = a (n) and b = b(n) depend on n. Precise bounds for the probability for local configurations to occur in a large ball are given. Under some conditions bearing on a (n) and b(n), the distance between copies of different local configurations is estimated according to their weights. Finally, a sufficient condition ensuring that a given local configuration occu...
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作者：Hitczenko, Pawel; Wesolowski, Jacek
作者单位：Drexel University; Warsaw University of Technology
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作者：Ethier, S. N.; Lee, Jiyeon
作者单位：Utah System of Higher Education; University of Utah; Yeungnam University
摘要：The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here, we evaluate the stationary distribution of the Markov chain, and this leads to a strong law of large numbers and a central limit theorem for the ...
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作者：Yu, Feng; Etheridge, Alison; Cuthbertson, Charles
作者单位：University of Bristol; University of Oxford; Morgan Stanley
摘要：We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size N. We show that regardless of mutation rates, as long as the proportion of beneficial mutations is strictly positive, the adaptation rate is at least O(log(1-delta) N) where delta can be any small positive number, if the population size is sufficiently large. This shows that if th...
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作者：Ichiba, Tomoyuki; Karatzas, Ioannis
作者单位：University of California System; University of California Santa Barbara
摘要：We examine the behavior of n Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient conditions are established for the absence and for the presence of triple collisions among the particles. As an application to the Atlas model for equity markets, we study a special construction of such systems of diffusing particles using Brownian motions with reflect...
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作者：Atchade, Yves F.
作者单位：University of Michigan System; University of Michigan
摘要：There is a growing interest in the literature for adaptive Markov chain Monte Carlo methods based on sequences of random transition kernels {P-n} where the kernel P-n is allowed to have an invariant distribution pi(n) not necessarily equal to the distribution of interest pi (target distribution). These algorithms are designed such that as n -> infinity, P-n converges to P. a kernel that has the correct invariant distribution pi. Typically, P is a kernel with good convergence properties, but on...
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作者：Jenkins, Paul A.; Song, Yun S.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the popu...
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作者：Barlow, Martin T.; Zheng, Xinghua
作者单位：University of British Columbia; Hong Kong University of Science & Technology
摘要：We consider a random walk in an lid. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for p(n)(omega)2(t)(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for p(n)(omega)2(t) (x, y) for all x, y in a ball.
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作者：Mischaikow, Konstantin; Wanner, Thomas
作者单位：Rutgers University System; Rutgers University New Brunswick; George Mason University
摘要：Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only through experimental observation or numerical simulations. In both cases, the data on which the topological measurements are based are derived via some form of finite sampling or discretization. In this paper, we present a probabilistic approach to quantifying the...
