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作者：Houdre, Christian; Talata, Zsolt
作者单位：University System of Georgia; Georgia Institute of Technology; University of Kansas
摘要：The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate of log n/root n is obtained. The uniform binary case is further explored, and an improved 1/root n rate obtained.
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作者：Martinelli, Fabio; Sinclair, Alistair
作者单位：Roma Tre University; University of California System; University of California Berkeley
摘要：We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of (O) over tilde (n(3.5)), which is tight within a factor of (O) over tilde(root n). The proof, which in addition gives some insight into the actual evolut...
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作者：Belius, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：This note investigates cover levels of finite sets in the random interlacements model introduced in [Ann. of Math. (2) 171 (2010) 2039-2087], that is, the least level such that the set is completely contained in the random interlacement at that level. It proves that as the cardinality of a set goes to infinity, the resealed and recentered cover level tends in distribution to the Gumbel distribution with cumulative distribution function exp(-exp(-z)).
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作者：Borrello, Davide
作者单位：University of Milano-Bicocca; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of Z(d). In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites. We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the ...
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作者：Gloria, Antoine; Otto, Felix
作者单位：Max Planck Society
摘要：This paper is the companion article to [Ann. Probab. 39 (2011) 779-856]. We consider a discrete elliptic equation on the d-dimensional lattice Z(d) with random coefficients A of the simplest type: They are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. This symmetric homogenized ma...
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作者：Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：We derive the asymptotic distribution of the total length L-n of a Beta(2 - alpha, alpha)-coalescent tree for 1 < alpha < 2, starting from n individuals. There are two regimes: If alpha 1/2(1 + root 5), then L-n suitably resealed has a stable limit distribution of index alpha. Otherwise L-n just has to be shifted by a constant (depending on n) to get convergence to a nondegenerate limit distribution. As a consequence, we obtain the limit distribution of the number S-n of segregation sites. The...
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作者：Basdevant, Anne-Laure; Singh, Arvind
作者单位：Universite Paris Saclay; Universite Paris Saclay
摘要：We consider a continuous-time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighboring vertex with rate proportional to the local time at that vertex plus a constant c. The walk is either transient or recurrent depending on this parameter c. In this paper, we complete results previously obtained by Davis and Volkov [Probab. Theory Related Fields 123 (2002) 281-300, Probab. Theory Related Fields...
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作者：Riordan, Oliver; Warnke, Lutz
作者单位：University of Oxford
摘要：It is widely believed that certain simple modifications of the random graph process lead to discontinuous phase transitions. In particular, starting with the empty graph on n vertices, suppose that at each step two pairs of vertices are chosen uniformly at random, but only one pair is joined, namely, one minimizing the product of the sizes of the components to be joined. Making explicit an earlier belief of Achlioptas and others, in 2009, Achlioptas, D'Souza and Spencer [Science 323 (2009) 145...
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作者：Bhamidi, Shankar; van der Hofstad, Remco
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of random edge lengths or costs on the geometry and flow transporting properties of the network. Two different regimes are of great interest, the weak disorder regime where optimality of a path is determined by the sum of edge weights on the path and the strong d...
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作者：Knispel, Thomas
作者单位：Leibniz University Hannover
摘要：For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter lambda epsilon (0, 1). Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a robust large deviations criter...
