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作者：GINE, E; ZINN, J
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：It is proved that, for h measurable and symmetric in its arguments and X(i) i.i.d., if the sequence (n(-m/2)SIGMA(i1,...,im less-than-or-equal-to n, ij not-equal ik if j not-equal k) h(X(i1),...,X(im))}n=1infinity is stochastically bounded, then Eh2 < infinity and Eh(X1,x2,...,x(m)) = 0 a.s..
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作者：BETZ, C; GZYL, H
摘要：By using an appropriate martingale, we compute the joint distribution of the hitting time and place of a sphere by d-dimensional Brownian motion, when the process starts outside the sphere.
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作者：ROSENTHAL, JS
摘要：We analyze a random walk on the orthogonal group SO(N) given by repeatedly rotating by a fixed angle through randomly chosen planes of R(N). We derive estimates of the rate at which this random walk will converge to Haar measure on SO(N), using character theory and the upper bound lemma of Diaconis and Shashahani. In some cases we are able to establish the existence of a ''cut off phenomenon'' for the random walk. This is the first such non-trivial result on a nonfinite group.
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作者：GOEL, PK; HALL, P
作者单位：Australian National University
摘要：For a sequence of bivariate pairs (X(i), Y(i)), the concomitant Y[i] of the ith largest x-value X(i) equals that value of Y paired with X(i). In assessing the quality of a file-merging or file-matching procedure, the penalty for incorrect matching may often be expressed as the average value of a function of the difference Y[i] - Y(i). We establish strong laws and central limit theorems for such quantities. Our proof is based on the observation that if G(x)(.) denotes the distribution function ...
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作者：ALBIN, JMP
作者单位：Lund University; Chalmers University of Technology
摘要：We give a complete and rather explicit characterization of the upper and lower classes for a family of stationary Gaussian stochastic processes.
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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：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：BENJAMINI, I; PERES, Y
作者单位：Yale University
摘要：We study a variant of branching Markov chains in which the branching is governed by a fixed deterministic tree T rather than a Galton-Watson process. Sample path properties of these chains are determined by an interplay of the tree structure and the transition probabilities. For instance, there exists an infinite path in T with a bounded trajectory iff the Hausdorff dimension of T is greater than log(1/rho) where rho is the spectral radius of the transition matrix.
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作者：CHAMAYOU, JF; LETAC, G
摘要：Let X1 be a (d x d) random stochastic matrix such that the rows of X1 are independent, with Dirichlet distributions. The rows of the (d x d) matrix A are the parameters of these Dirichlet distributions, and we assume that the sums of the rows and columns of A provide the same vector r = (r1,...,r(d)). If (X(n))(n=1)infinity are i.i.d., we prove that lim(n-->infinity)(X(n)...X1) almost surely has identical rows, which are Dirichlet distributed with parameter r. Van Assche has proved this for d ...
