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作者：Jagannath, Aukosh; Ko, Justin; Sen, Subhabrata
作者单位：University of Toronto; Stanford University
摘要：We study the asymptotic behavior of the Max kappa-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi-type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.
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作者：Pitman, Jim; Yakubovich, Yuri
作者单位：University of California System; University of California Berkeley; Saint Petersburg State University; Saint Petersburg State University
摘要：We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(alpha, theta) random discrete distribution on the positive integers. These frequencies are a (size-alpha)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavare [Adv. in Appl. Probab.18 (1986) 1-19] for al...
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作者：Bernardin, Cedric; Goncalves, Patricia; Jara, Milton
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universidade de Lisboa
摘要：We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant, energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric Levy process. For a critical value of the coupling, the energy diffusion is described by a family of Levy processes which interpolate between these two processes.
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作者：Swart, Jan M.
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching or...
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作者：Thacker, Debleena; Volkov, Stanislav
作者单位：Lund University
摘要：Start with a graph with a subset of vertices called the border. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number xi of particles to be released by this final moment. We show...
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作者：Hening, Alexandru; Nguyen, Dang H.
作者单位：Tufts University; Wayne State University
摘要：In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n populations that live in a stochastic environment and which can interact nonlinearly (through com...
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作者：Ding, Xiucai; Yang, Fan
作者单位：University of Toronto; University of Wisconsin System; University of Wisconsin Madison
摘要：In this paper, we prove a necessary and sufficient condition for the edge universality of sample covariance matrices with general population. We consider sample covariance matrices of the form Q = TX(TX)*, where X is an M-2 x N random matrix with X-ij = N-1/2 qij such that qij are i.i.d. random variables with zero mean and unit variance, and T is an M-1 x M-2 deterministic matrix such that T*T is diagonal. We study the asymptotic behavior of the largest eigenvalues of Q when M := min{M-1 x M-2...
