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作者：Hahn, MG; Klass, MJ
作者单位：Tufts University; University of California System; University of California Berkeley
摘要：This paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary lid. random variables. The introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary lid. random variables. More specifically, let n be a fixed natural number and let Z, Z(1), Z(2),..., Z(n) be arbitrary i.i.d. random variables We construct a function F-Z,F- n(a), derived from the probabi...
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作者：Ben Arous, G; Guionnet, A
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the averaged law of the empirical measure on the path space of these dynamics satisfies a large deviation upper bound in the high temperature regime. We study the rate function which governs this large deviation upper bound and prove that it achieves its minimum value at a unique probability measure Q which is not Markovian: We deduce an ave...
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作者：van den Berg, J
作者单位：Centrum Wiskunde & Informatica (CWI)
摘要：For spin systems with random, finite-range interactions, we define an analog of the usual weak mixing property, which we call weak mixing in expectation (WME). This property implies (almost sure) uniqueness of the Gibbs measure. We concentrate on the two-dimensional case, for which we present finite-volume conditions which are sufficient for WME. We also show the reverse: if the system is WME, then the condition is satisfied for some (sufficiently large) volume. Simultaneously, we obtain an ex...
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作者：Bhattacharya, RN; Lee, O
作者单位：Indiana University System; Indiana University Bloomington
摘要：The set P(S) of probability measures on the Borel sigma field of every closed subset S of R-k is shown to be complete under a Kolmogorov type metric. An assertion in the 1988 article by Bhattacharya and Lee that this completeness holds if S is merely topologically complete is false.
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作者：Fernandez, R; Pfister, CE
作者单位：Universidade de Sao Paulo; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the question of whether the quasilocality (continuity, almost Markovianness) property of Gibbs measures remains valid under a projection on a sub-sigma-algebra. Our method is based on the construction of global specifications, whose projections yield local specifications for the projected measures. For Gibbs measures compatible with monotonicity preserving local specifications, we show that the set of configurations where quasilocality is lost is an event of the tail field. This set i...
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作者：Bolthausen, E; den Hollander, F
作者单位：University of Zurich; Radboud University Nijmegen
摘要：Consider the directed process (i, S-i)(i greater than or equal to 0) where the second component is simple random walk on Z (S-0 = 0). Define a transformed path measure by weighting each n-step path with a factor exp[lambda Sigma(1 less than or equal to i less than or equal to n) (omega(i) + h)sign(S-i)]. Here, (omega(i))(i greater than or equal to 1) is an i.i.d. sequence of random variables taking values +/- 1 with probability 1/2 lading as a random medium), while lambda is an element of [0, ...
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作者：Gnedin, AV
作者单位：University of Gottingen
摘要：A composition structure is a sequence of consistent probability distributions for compositions(ordered partitions) of n = 1, 2,.... Any composition structure can be associated with an exchangeable random composition of the set of natural numbers. Following Donnelly and Joyce, we study the problem of characterizing a generic composition structure as a convex mixture of the extreme ones. We topologize the family u of open subsets of [0, 1] so that u becomes compact and show that u is homeomorphi...
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作者：Schied, A
作者单位：Humboldt University of Berlin
摘要：This paper is concerned with the intrinsic metrics of the two main classes of superprocesses. For the Fleming-Viot process, we identify it as the Bhattacharya distance, and for Dawson-Watanabe processes, we find the Kakutani-Hellinger metric. The corresponding geometries are studied in some detail. In particular, representation formulas for geodesics and are length functionals are obtained. The relations between the two metrics yield a geometric interpretation of the identification of the Flem...
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作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Lund University
摘要：Let X-1, Y-1, Y-2,..., X-n, Y-n be independent nonnegative rv's and let {b(ij)}(1 less than or equal to i, j less than or equal to n) be an array of nonnegative constants. We present a method of obtaining the order of magnitude of E Phi (Sigma(1 less than or equal to i, j less than or equal to n) b(ij) X-i Y-j), for any such {X-i}, {Y-i} and {b(ij)} and any nondecreasing function Phi on [0, infinity) with Phi(0) = 0 and satisfying a Delta(2) growth condition Furthermore, this technique is exte...
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作者：Hambly, BM
作者单位：University of Edinburgh
摘要：We introduce a random recursive fractal based on the Sierpinski gasket and construct a diffusion upon the fractal via a Dirichlet form. This form and its symmetrizing measure are determined by the electrical resistance of the fractal. The effective resistance provides a metric with which to discuss the properties of the fractal and the diffusion. The main result is to obtain uniform upper and lower bounds for the transition density of the Brownian motion on the fractal in terms of this metric....
