The Annals of Probability

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• IBM, SIBM and IBS AI翻译
  作者：Verzani, J; Adler, R
  作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
  摘要：We construct a super iterated Brownian motion (SIBM) from a historical version of iterated Brownian motion (IBM) using an iterated Brownian snake (IBS). It is shown that the range of super iterated Brownian motion is qualitatively quite different from that of super Brownian motion in that there are points with explosions in the branching. However, at a fixed time the support of SIBM has an exact Hausdorff measure function that is the same (up to a constant) as that of super Brownian motion at ...
• Robust phase transitions for Heisenberg and other models on general trees AI翻译
  作者：Pemantle, R; Steif, JE
  作者单位：University of Wisconsin System; University of Wisconsin Madison; Chalmers University of Technology
  摘要：We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the interactions are proportional to the cosines of the angles between neighboring spins. The phenomenon of interest here is the classification of phase transition (nonuniqueness of the Gibbs state) according to whether it is robust. in many cases, including all of the Heisenberg and Potts models, occurr...
• Sylvester's question: The probability that n points are in convex position AI翻译
  作者：Bárány, I
  作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London
  摘要：For a convex body K in the plane, let p(n, K) denote the probability that n random, independent, and uniform points from K are in convex position, that is, none of them lies in the convex hull of the others. Here we determine the asymptotic behavior of p(n, K) by showing that, as n goes to infinity, n(2) (n)root(p(n, K)) tends to a finite and positive limit.
• Ballot theorems and sojourn laws for stationary processes AI翻译
  作者：Kallenberg, O
  作者单位：Auburn University System; Auburn University
  摘要：The ballot theorem and the uniform law for sojourn times, both results known for cyclically stationary sequences and processes on a bounded index set, are here extended to infinite, stationary sequences and to stationary processes on R+. Our extensions contain all previously known versions as special cases.
• Ratio limit theorems for a Brownian motion killed at the boundary of a Benedicks domain AI翻译
  作者：Collet, P; Martínez, S; San Martín, J
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile
  摘要：We consider a Brownian motion in a Benedicks domain with absorption at the boundary. We show ratio limit theorems for the associated heat kernel. When the hole is compact, therefore the Martin boundary is two dimensional; we obtain sharp estimates on the lifetime probabilities and we identify, in probabilistic terms, the various constants appearing in the theory.
• Central limit theorems for the Wasserstein distance between the empirical and the true distributions AI翻译
  作者：Del Barrio, E; Giné, E; Matrán, C
  作者单位：Universidad de Valladolid; University of Connecticut
  摘要：If X is integrable, F is its cdf and F-n is the empirical cdf based on an i.i.d. sample from F, then the Wasserstein distance between F-n and F, which coincides with the L-1 norm integral(-infinity)(infinity)\F-n(t) - F(t)\ dt of the centered empirical process, tends to zero a.s. The object of this article is to obtain rates of convergence and distributional limit theorems for this law of large numbers or, equivalently, stochastic boundedness and distributional limit theorems for the L-1 norm ...
• The second lowest extremal invariant measure of the contact process II 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 continue the investigation of the behavior of the contact process on infinite connected graphs of bounded degree. Some questions left open by Salzano and Schonmann (1997) concerning the notions of complete convergence, partial convergence and the criterion r = s are answered. The continuity properties of the survival probability and the recurrence probability are studied. These order parameters are found to have a richer behavior than expected, with the possibility of the survival probabili...
• Coexistence in threshold voter models (vol 22, pg 764, 1994) AI翻译
  作者：Liggett, TM
  作者单位：University of California System; University of California Los Angeles
• Optimum bounds for the distributions of martingales in Banach spaces (vol 22, pg 1679, 1994) AI翻译
  作者：Pinelis, I
• Typical configurations for one-dimensional random field Kac model AI翻译
  作者：Cassandro, M; Orlandi, E; Picco, P
  作者单位：Sapienza University Rome; Roma Tre University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we study the typical profiles of a random field Kac model. We give upper and lower bounds of the space scale where the profiles are constant. The results hold almost surely with respect to the realizations of the random field. The analysis is based on a block-spin construction, deviation techniques for the local empirical order parameters and concentration inequalities for the realizations of the random magnetic field. For the upper bound, we exhibit a scale related to the law of...