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最新文章

• Stability of the overshoot for Levy processes AI翻译
  作者：Doney, RA; Maller, RA
  作者单位：University of Manchester; University of Western Australia
  摘要：We give equivalences for conditions like X (T (r))/r -->1 and X (T*(r))/ r --> 1, where the convergence is in probability or almost sure, both as r --> 0 and r --> infinity, where X is a Levy process and T(r) and T*(r) are the first exit times of X out of the strip {(t, y) : t > 0,\y\ < r} and half-plane {(t, y) : t > 0, y less than or equal to r}, respectively. We also show, using a result of Kesten, that X(T*(r))/r --> 1 a.s. as r --> 0 is equivalent to X creeping across a level.
• On the high temperature phase of the Sherrington-Kirkpatrick model AI翻译
  作者：Talagrand, M
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：We prove the validity of the replica-symmetric solution of the Sherrington-Kirkpatrick model in a region that (probably) coincides with the region predicted by the physicists.
• Strict positivity of the density for simple jump processes using the tools of support theorems. Application to the Kac equation without cutoff AI翻译
  作者：Fournier, N
  作者单位：Universite de Lorraine
  摘要：Consider the one-dimensional solution X = {X-t}(tis an element of[0,T]) of a possibly degenerate stochastic differential equation driven by a (non compensated) Poisson measure. We denote by M a set of deterministic integer-valued measures associated with the considered Poisson measure. For in m is an element of M, we denote by S(m) = {S-t(m)}(tis an element of[0,T]) the skeleton associated with X. We assume some regularity conditions, which allow to define a sort of derivative DSt (m) of S-t (...
• On the nonuniqueness of the invariant probability for i.i.d. random logistic maps AI翻译
  作者：Athreya, KB; Dai, JJ
  作者单位：Iowa State University
  摘要：Let {X-n}(0)(infinity) be a Markov chain with values in [0, 1] generated by the iteration of random logistic maps defined by Xn+1 = f(Cn+1) (X-n) equivalent to Cn+1 X-n (1 - X-n), n = 0, 1, 2,..., with {C-n}(1)(infinity) being independent and identically distributed random variables with values in [0, 4] and independent of X-0. This paper provides a class of examples where C-i take only two values lambda and mu such that there exist two distinct invariant probability distributions pi(0) and pi...
• Gaussian limit for determinantal random point fields AI翻译
  作者：Soshnikov, A
  作者单位：University of California System; University of California Davis
  摘要：We prove that, under fairly general conditions, a properly rescaled determinantal random point field converges to a generalized Gaussian random process.
• Explicit isoperimetric constants and phase transitions in the random-cluster model AI翻译
  作者：Häggström, O; Jonasson, J; Lyons, R
  作者单位：University of Gothenburg; Indiana University System; Indiana University Bloomington; Chalmers University of Technology
  摘要：The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster parameter q greater than or equal to 1. Among these, the main ones are the absence of percolation for the free random-cluster measure at the critical value and examples of planar regular graphs with regular dual where p(c)(free)(q) > p(u)(wired)(q) for q large enoug...
• On the distribution of the square integral of the Brownian bridge AI翻译
  作者：Tolmatz, L
  摘要：Smirnov obtained the distribution F for his omega(2)-test in the form of a certain series. F is identical to the distribution of the the Brownian bridge in the L-2 norm. Smirnov, Kac and Shepp determined the Laplace-Stieltjes transform of F. Anderson and Darling expressed F in terms of Bessel functions. In the present paper we compute the moments of F and their asymptotics, obtain expansions of F and its density f in terms of the parabolic cylinder functions and Laguerre functions, and determi...