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作者：Jia, Chen; Jiang, Da-Quan; Qian, Min-Ping
作者单位：Chinese Academy of Engineering Physics; Beijing Computational Science Research Center (CSRC); Peking University; Peking University
摘要：In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov chains. Moreover, we use these cycle symmetries to study the circulation fluctuations for Markov chains. We prove that the sample circulations along a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has a highly nonobvious symmetry. Further extensions and appli...
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作者：Hackmann, Daniel; Kuznetsov, Alexey
作者单位：York University - Canada
摘要：Levy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Levy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in [Int. J. Theor. Appl. Finance 13 (2010) 63-91, Quant. Finance 10 (2010) 629-644] and develop a simple yet very efficient method for approximating processes with completely monotone jumps by...
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作者：Whiteley, Nick; Lee, Anthony
作者单位：University of Bristol; University of Warwick
摘要：We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to hidden Markov models, we show how to sample exactly from the finite-dimensional conditional distributions of the signal process given infinitely many observations, using an algorithm which requires only an almost surely finite number of observations to actua...
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作者：Basu, Riddhipratim; Holroyd, Alexander E.; Martin, James B.; Wastlund, Johan
作者单位：Stanford University; Microsoft; University of Oxford; Chalmers University of Technology
摘要：We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with optimal play on percolation clusters of Euclidean lattices. On Z(2) with two different percolation parameters for odd and even sites, we prove that the game has no draws provided closed sites of one parity are sufficiently rare compared with those of the ot...
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作者：Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Institute of Science & Technology - Austria
摘要：We consider sample covariance matrices of the form Q = (Sigma X-1/2)((EX)-X-1/2)*, where the sample X is an M x N random matrix whose entries are real independent random variables with variance 1/N and where Sigma is an M x M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest resealed eigenvalue of Q when both M and N tend to infinity with N/M -> d is an element of (0, infinity). For a large class of populations Sigma in the sub-critical regime, we sh...
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作者：Lucon, Eric; Stannat, Wilhelm
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Technical University of Berlin
摘要：We consider a system of N disordered mean-field interacting diffusions within spatial constraints: each particle theta(i) is attached to one site x(i) of a periodic lattice and the interaction between particles theta(i) and theta(j) decreases as vertical bar x(i) - x(j)vertical bar(-alpha) for alpha is an element of [0, 1). In a previous work [Ann. Appl. Probab. 24 (2014) 1946-1993], it was shown that the empirical measure of the particles converges in large population to the solution of a non...
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作者：Arapostathis, Ari; Pang, Guodong
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We consider Markovian multiclass multi-pool networks with heterogeneous server pools, each consisting of many statistically identical parallel servers, where the bipartite graph of customer classes and server pools forms a tree. Customers form their own queue and are served in the first-come first served discipline, and can abandon while waiting in queue. Service rates are both class and pool dependent. The objective is to study the limiting diffusion control problems under the long run averag...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Sorbonne Universite
摘要：We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the q-Hahn TASEP and the q-Hahn Boson (zero-range) process introduced in [J. Phys. A 46 (2013) 465205, 25] and further studied in [Int. Math. Res. Not. IMRN 14 (2015) 5577-5603], by allowing jumps in both directions. Owing to a Markov duality, we prove moment formulas for the locations of particles in the exclusion process. This leads to a Fredholm determinant formula that characterize...
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作者：Mossel, Elchanan; Neeman, Joe; Sly, Allan
作者单位：University of Pennsylvania; University of California System; University of California Berkeley; University of Bonn; University of Texas System; University of Texas Austin; Australian National University
摘要：We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a/n and b/n for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better than a random guess if and only if (a - b)(2) > 2(a b). Using a variant of belief propagation, we give a reconstruction algorithm that is optimal in the sense that if (a - b)(2) > C (a b) for some constant C then our algorithm maximizes the fraction of the nodes ...
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作者：Cox, J. Theodore; Peres, Yuval; Steif, Jeffrey E.
作者单位：Syracuse University; Microsoft; Chalmers University of Technology; University of Gothenburg
摘要：Given a continuous time Markov Chain {q (x, y)} on a finite set S, the associated noisy voter model is the continuous time Markov chain on {0, 1}(S), which evolves in the following way: (1) for each two sites x and y in S, the state at site x changes to the value of the state at site y at rate q (x, y); (2) each site rerandomizes its state at rate 1. We show that if there is a uniform bound on the rates {q (x, y)} and the corresponding stationary distributions are almost uniform, then the mixi...
