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作者：Cotar, Codina; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We consider two versions of random gradient models. In model A the interface feels a bulk term of random fields while in model B the disorder enters through the potential acting on the gradients. It is well known that for gradient models without disorder there are no Gibbs measures in infinite-volume in dimension d = 2, while there are gradient Gibbs measures describing an infinite-volume distribution for the gradients of the field, as was shown by Funaki and Spohn. Van Enter and Kulske proved...
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作者：Arguin, Louis-Pierre; Bovier, Anton; Kistler, Nicola
作者单位：Universite de Montreal; University of Bonn
摘要：As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time t, extremal particles descend with overwhelming probability from ancestors having split either within a distance of order 1 from time 0, or within a distance of order 1 from time t. The result suggests that the extremal process of branching Brownian motion is a randomly shifted cluster p...
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作者：Berestycki, Nathanael; Pymar, Richard
作者单位：University of Cambridge
摘要：We consider bond percolation on n vertices on a circle where edges are permitted between vertices whose spacing is at most some number L = L(n). We show that the resulting random graph gets a giant component when L >> (log n)(2) (when the mean degree exceeds 1) but not when L << log n. The proof uses comparisons to branching random walks. We also consider a related process of random transpositions of n particles on a circle, where transpositions only occur again if the spacing is at most L. Th...
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作者：Jiang, Yunjiang
作者单位：Stanford University
摘要：We show that the classical Kac's random walk on (n - 1)-sphere Sn-1 starting from the point mass at e(1) mixes in O(n(5)(log n)(3)) steps in total variation distance. The main argument uses a truncation of the running density after a burn-in period, followed by L-2 convergence using the spectral gap information derived by other authors. This improves upon a previous bound by Diaconis and Saloff-Coste of order O(n(2n)).
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作者：Griffin, Philip S.; Maller, Ross A.
作者单位：Syracuse University; Australian National University; Australian National University
摘要：We analyze the general Levy insurance risk process for Levy measures in the convolution equivalence class S-(alpha), alpha > 0, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level u -> infinity, and a host of new results for functionals of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as u > infinity, conditional on ruin occurring under our ...
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作者：Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
作者单位：University of Munich; Princeton University; Goethe University Frankfurt
摘要：On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the implicit Euler scheme is known to converge strongly to the exact solution of such an SDE. Implementations of the implicit Euler scheme, however, require additional computational effort. In this article we therefore propose an explicit and easily i...
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作者：Litterer, C.; Lyons, T.
作者单位：Imperial College London; University of Oxford; University of Oxford
摘要：Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynam...
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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：Garet, Olivier; Marchand, Regine
作者单位：Universite de Lorraine
摘要：The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H-t denotes the set of already occupied sites at time t, we show that for almost every environment, when the contact process survives, the set H-t/t almost surely converges to a compact set that only depends on the law of the environment. To this aim, we prove a new almost subadditive...
