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作者：Wang, Yizao; Roy, Parthanil; Stoev, Stilian A.
作者单位：University of Michigan System; University of Michigan; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：We establish characterization results for the ergodicity of stationary symmetric alpha-stable (S alpha S) and alpha-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in the multiparameter setting, that is, a stationary S alpha S (0 < alpha < 2) random field is ergodic (or, equivalently, weakly mixing) if and only if it is generated by a null group action. Similar results are also established for max-stable random fields. The key in...
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作者：Cator, Eric; Pimentel, Leandro P. R.
作者单位：Delft University of Technology; Universidade Federal do Rio de Janeiro
摘要：In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89-125], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process or the Hammersley interacting particle process. The method will be to use the well-known last-passage p...
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作者：Jung, Paul; Markowsky, Greg
作者单位：University of Alabama System; University of Alabama Birmingham; Monash University
摘要：For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the so-called iterated Brownian motion. Khoshnevisan and Lewis [Ann. Appl. Probab. 9 (1999) 629-667] suggested the existence of a form of measure-theoretic duality between iterated Brownian motion and a Brownian motion in random scenery. We show that a random walk ...
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作者：Sabot, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d >= 3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result ...
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作者：Calka, Pierre; Schreiber, Tomasz; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Nicolaus Copernicus University; Lehigh University
摘要：Schreiber and Yukich [Ann. Probab. 36 (2008) 363-396] establish an asymptotic representation for random convex polytope geometry in the unit ball B-d, d >= 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional limit theorems for th...
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作者：Dembo, Amir; Montanari, Andrea; Sun, Nike
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density phi, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity phi subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we co...
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper, we show that reflecting Brownian motion in any bounded domain D can be approximated, as k -> infinity, by simple random walks on maximal connected subsets of (2(-k)Z(d)) boolean AND D whose filled-in interiors are inside of D.
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作者：Deroin, B.; Kleptsyn, V.; Navas, A.; Parwani, K.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universidad de Santiago de Chile; Eastern Illinois University
摘要：We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of global stability at a finite distance: roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns t...
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作者：Duminil-Copin, H.; Van Enter, A. C. D.
作者单位：University of Geneva; University of Groningen
摘要：Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following anisotropic boot-strap percolation model: the neighborhood of a point (m, n) is the set {(m + 2, n), (m + 1, n), (m, n + 1), (m - 1, n), (m - 2, n), (m, n - 1)}. At time 0, sites are occupied with probability p. At each time step, sites that are occupied remain occupied, while sites that are not occupied become occupied if and only if three of more sites in their neig...
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作者：Kabluchko, Zakhar; Zaporozhets, Dmitry
作者单位：Ulm University; Russian Academy of Sciences
摘要：It has been shown by Ibragimov and Zaporozhets [In Prokhorov and Contemporary Probability Theory (2013) Springer] that the complex roots of a random polynomial G(n)(z) = Sigma(n)(k=0) xi(k)z(k) with i.i.d. coefficients xi(0), ... , xi(n) concentrate a.s. near the unit circle as n -> infinity if and only if E log(+)vertical bar xi(0)vertical bar < infinity. We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like L(log vertical ...
