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作者：CHAN, T
摘要：This note studies the deterministic flow of measures which is the limiting case as n --> infinity of Dyson's model of the motion of the eigenvalues of random symmetric n x n matrices. Though this flow is nonlinear, highly singular and apparently of Wiener-Hopf type, it may be solved explicitly without recourse to Wiener-Hopf theory. The solution greatly clarifies the role of the famous Wigner semicircle law.
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作者：BARTOSZEK, W
摘要：Let (xi n)(n greater than or equal to 0) be a random walk on a countable group G. Sufficient and necessary conditions for the existence of a finite set A subset of or equal to G and a sequence g(n) is an element of G such that for all natural n we have P(xi(n) is an element of A/xi(0) = g(n)) = 1 are presented. This provides a complete solution to the problem of behavior of concentration functions on discrete groups.
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作者：BEZUIDENHOUT, C; GRAY, L
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We study a class of attractive spin systems. We prove that for these processes the system dies out when the parameters are on the critical surface. We also prove that the supercritical process survives with positive probability in a sufficiently thick space-time ''slab.''
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作者：MADRAS, N; SCHINAZI, R; SCHONMANN, RH
作者单位：University of Colorado System; University of Colorado at Colorado Springs; University of California System; University of California Los Angeles
摘要：We consider the contact process with inhomogeneous deterministic death rates. We prove the following: 1. Such models may have discontinuous transitions, in the sense of surviving at the critical point. 2. If the death rates are identically 1, except on a set which is small enough in a proper sense and where the death rates take a fixed value smaller than 1, then the critical point is identical to that of the homogeneous system. Extensions of the results to other (d + 1)-dimensional systems wit...
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作者：VANDENBERG, J; MAES, C
摘要：Recently, one of the authors (van den Berg) has obtained a uniqueness condition for Gibbs measures, in terms of disagreement percolation involving two independent realizations. In the present paper we study the dependence of Markov fields on boundary conditions by taking a more suitable coupling. This coupling leads to a new uniqueness condition, which improves the one mentioned above. We also compare it with the Dobrushin uniqueness condition. In the case of the Ising model, our coupling shar...
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作者：XIANG, XJ
作者单位：University of Chicago
摘要：In this article we derive a law of the logarithm for the maximal deviation between two kernel-type quantile density estimators and the true underlying quantile density function in the randomly right-censored case. Extensions to higher derivatives are included. The results are applied to get optimal bandwidths with respect to almost sure uniform convergence.
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作者：DEUSCHEL, JD
摘要：We consider a special class of attractive critical processes based on the transition function of a transient random walk on Z(d). These processes have infinitely many invariant distributions and no spectral gap. The exponential L2 decay is replaced by an algebraic L2 decay. The paper shows the dependence of this algebraic rate in terms of the dimension of the lattice and the locality of the functions under consideration. The theory is illustrated by several examples dealing with locally intera...
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作者：BRAMSON, M; NEUHAUSER, C
作者单位：University of Southern California
摘要：Cellular automata have been the subject of considerable recent study in the statistical physics literature, where they provide examples of easily accessible nonlinear phenomena. We investigate a class of nearest neighbor cellular automata taking values {0, 1} on Z. In the deterministic setting, this class includes rules which yield fractal-like patterns when starting from a single occupied site. We are interested here in the asymptotic behavior of systems subjected to small random perturbation...
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作者：KNIGHT, FB; MAISONNEUVE, B
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Let R be a random time in F-infinity, the terminal element of a filtration F-t satisfying the usual hypotheses. It is shown that if optional sampling holds at R for all bounded martingales, then R is optional. If F-t is the natural pseudo-path filtration of a measurable process X(t), then R is optional if (and only if) the conditional distribution of X(R+), given F-R is Z(R), where Z(t) is an optional version of the conditional distribution of X(t+), given F-t.
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作者：SEPPALAINEN, T
摘要：This paper presents almost sure uniform large deviation principles for the empirical distributions and empirical processes of Markov chains with random transitions. The results are derived under assumptions that generalize assumptions earlier used for time-homogeneous chains. The rate functions for the skew chain are expressed in terms of the Donsker-Varadhan functional and relative entropy The sample chain rates are different, but they have natural upper and lower bounds in terms of familiar ...
