The Annals of Probability

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• An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space AI翻译
  作者：Bobkov, SG
  作者单位：Syktyvkar State University
  摘要：We prove an isoperimetric inequality on the discrete cube which is the precise analog of a logarithmic inequality due to Talagrand. As a consequence, the Gaussian isoperimetric inequality is derived.
• Asymptotics of a class of Markov processes which are not in general irreducible (vol 16, pg 1333, 1988) AI翻译
  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.
• When is a probability measure determined by infinitely many projections? AI翻译
  作者：Bélisle, C; Massé, JC; Ransford, T
  作者单位：Laval University
  摘要：The well-known Cramer-Wold theorem states that a Borel probability measure on R-d is uniquely determined by the totality of its one-dimensional projections. In this paper we examine various conditions under which a probability measure is determined by a subset of its (d - 1)-dimensional orthogonal projections.
• Long time existence for the wave equation with a noise term AI翻译
  作者：Mueller, C
  作者单位：University of Rochester
  摘要：We consider the equation u(tt) = Delta u + a(u)N for x is an element of R-1 or R-2. N is a Gaussian noise term, which is white noise if x is an element of R-1. If a(u) grows no faster than u(log u)(1/2-epsilon), then there is a unique solution valid for all time.
• The second lowest extremal invariant measure of the contact process AI翻译
  作者：Salzano, M; Schonmann, RH
  作者单位：University of California System; University of California Los Angeles
  摘要：We study the ergodic behavior of the contact process on infinite connected graphs of bounded degree. We show that the fundamental notion of complete convergence is not as well behaved as it was thought to be. In particular there are graphs for which complete convergence holds in any number of separated intervals of values of the infection parameter and fails for the other values of this parameter. We then introduce a basic invariant probability measure related to the recurrence properties of t...
• Global specifications and nonquasilocality of projections of Gibbs measures AI翻译
  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...
• Localization transition for a polymer near an interface AI翻译
  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, ...
• The representation of composition structures AI翻译
  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...
• Geometric aspects of Fleming-Viot and Dawson-Watanabe processes AI翻译
  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...
• Brownian excursions, critical random graphs and the multiplicative coalescent AI翻译
  作者：Aldous, D
  作者单位：University of California System; University of California Berkeley
  摘要：Let(B-t(s), 0 less than or equal to s < infinity) be reflecting inhomogeneous Brownian motion with drift t - s at time s, started with B-t(0) = 0. Consider the random graph G(n, n(-1) + tn(-4/3)), whose largest components have size of order n(2/3) Normalizing by n(-2/3), the asymptotic joint distribution of component sizes is the same as the joint distribution of excursion lengths of Bt (Corollary 2). The dynamics of merging of components as t increases are abstracted to define the multiplicat...