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作者：Yogeshwaran, D.; Subag, Eliran; Adler, Robert J.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Weizmann Institute of Science; Technion Israel Institute of Technology
摘要：We consider the topology of simplicial complexes with vertices the points of a random point process and faces determined by distance relationships between the vertices. In particular, we study the Betti numbers of these complexes as the number of vertices becomes large, obtaining limit theorems for means, strong laws, concentration inequalities and central limit theorems. As opposed to most prior papers treating random complexes, the limit with which we work is in the so-called 'thermodynamic'...
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作者：Banerjee, Sayan; Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：Maximal couplings are (probabilistic) couplings of Markov processes such that the tail probabilities of the coupling time attain the total variation lower bound (Aldous bound) uniformly for all time. Markovian (or immersion) couplings are couplings defined by strategies where neither process is allowed to look into the future of the other before making the next transition. Markovian couplings are typically easier to construct and analyze than general couplings, and play an important role in ma...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider random interlacements on Z(d), d >= 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of large side-length from the boundary of a larger homothetic box. As a corollary, we obtain an asymptotic upper bound on a similar quantity, where the random interlacements are replaced by the simple random walk. It is plausible, but open at the moment, that these asymptotic upper bo...
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作者：Stauffer, Alexandre
作者单位：University of Bath
摘要：We study random triangulations of the integer points [0, n](2) boolean AND Z(2), where each triangulation has probability measure with being a real parameter and denoting the sum of the length of the edges in . Such triangulations are called lattice triangulations. We construct a height function on lattice triangulations and prove that, in the whole subcritical regime , the function behaves as a Lyapunov function with respect to Glauber dynamics; that is, the function is a supermartingale. We ...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions wher...
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作者：Ganguly, Shirshendu; Levine, Lionel; Peres, Yuval; Propp, James
作者单位：University of Washington; University of Washington Seattle; Cornell University; Microsoft; University of Massachusetts System; University of Massachusetts Lowell
摘要：We introduce a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get emitted from their respective bases and perform random walk. On encountering a particle of the opposite color they kill it and occupy its position. We prove that on the cylinder graph (the product of a path and a cycle) an interface spontaneously forms between red and blue and is main...
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作者：Kosygina, Elena; Zerner, Martin P. W.
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Eberhard Karls University of Tubingen
摘要：We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog models with i.i.d. numbers of frogs per site where the frog dynamics are given by quasi-transitive Markov chains or by random walks in a common random environment including super-critical percolation clusters on . We also give a sufficient and almost sharp condition for recurrence of uniformly elliptic frog processe...
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作者：Cerny, Jiri; Wassmer, Tobias
作者单位：University of Vienna
摘要：We study the Metropolis dynamics of the simplest mean-field spin glass model, the random energy model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen 'fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.
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作者：Hofmanova, Martina; Roeger, Matthias; von Renesse, Max
作者单位：Max Planck Society; Technical University of Berlin; Dortmund University of Technology; Leipzig University
摘要：We study a stochastically perturbed mean curvature flow for graphs in over the two-dimensional unit-cube subject to periodic boundary conditions. The stochastic perturbation is a one dimensional white noise acting uniformly in all points of the surface in normal direction. We establish the existence of a weak martingale solution. The proof is based on energy methods and therefore presents an alternative to the stochastic viscosity solution approach. To overcome difficulties induced by the dege...
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作者：Meiners, Matthias; Mentemeier, Sebastian
作者单位：Technical University of Darmstadt; Dortmund University of Technology
摘要：We consider smoothing equations of the form X law = Sigma(j >= 1) TjXj + C where is a given sequence of random variables and are independent copies of X and independent of the sequence . The focus is on complex smoothing equations, i.e., the case where the random variables are complex-valued, but also more general multivariate smoothing equations are considered, in which the are similarity matrices. Under mild assumptions on , we describe the laws of all random variables X solving the above sm...
