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作者：Lifshits, M; Shi, Z
作者单位：Saint Petersburg State University; Universite Paris Cite; Sorbonne Universite; Universite de Lille
摘要：We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L-n at any fixed time prior to the critical time. The asymptotic behavior of L-n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (cold gas) L-n has logarithmic order of growth while higher speeds (warm gas) yield pol...
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作者：Puhalskii, AA
作者单位：University of Colorado System; University of Colorado Denver
摘要：We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components and of the numbers of the excess edges of the giant components. For the supercritical case, we obtain the asymptotics of normal deviations and the logarithmic asymptotics of lar...
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作者：Anshelevich, M
作者单位：University of California System; University of California Riverside
摘要：Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom, we calculate and give an interpretation of linearization coefficients for a number of polynomial families. Th...
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作者：Holroyd, AE; Peres, Y
作者单位：University of British Columbia; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Let Pi be an ergodic simple point process on R-d and let Pi* be its Palm version. Thorisson [Ann. Probab. 24 (1996) 2057-2064] proved that there exists a shift coupling of Pi and Pi*; that is, one can select a (random) point Y of Pi such that translating Pi by -Y yields a configuration whose law is that of Pi*. We construct shift couplings in which Y and Pi* are functions of Pi and prove that there is no shift coupling in which Pi is a function of Pi*. The key ingredient is a deterministic tra...
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作者：Hsing, T; Rootzén, H
作者单位：University System of Ohio; Ohio State University; Chalmers University of Technology
摘要：This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X-1,..., X-Nn where X-1, X-2,... are i.i.d. in R-2 with distribution F and N-n is independent of the X-i and satisfies N-n/n --> (p) 1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded support. The general results are applied to a number of special cases, including elliptically co...
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作者：Ruzmaikina, A; Aizenman, M
作者单位：University of Virginia; Purdue University System; Purdue University; Purdue University System; Purdue University; Princeton University; Princeton University
摘要：We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. Quasi-stationary states are defined as probability measures, on the sigma-algebra generated by the gap variables, for which joint distribution of gaps between particles is invariant under the time evolution. Examples are provided by Poisson processes with densities of the form rho(dx) = e(-sx) sdx, with s > 0, and linear superpositions of such measures. We show that, convers...
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作者：Le Gall, JF; Mytnik, L
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Technion Israel Institute of Technology
摘要：This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1 + beta)-stable branching mechanism. It establishes the continuity of the density in dimension d = 2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutio...
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作者：Mikulevicius, R; Rozovskii, BL
作者单位：University of Southern California; University of Southern California
摘要：This paper concerns the Cauchy problem in R-d for the stochastic Navier-Stokes equation partial derivativetu = Deltau - (u, del)u - delp + f(u) + [(sigma, del)u - delp + g(u)] o W, u(0) = u(0), div u = 0, driven by white noise W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global stron...
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作者：Nualart, D; Peccati, G
作者单位：University of Barcelona; Sorbonne Universite
摘要：We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes.
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作者：Albeverio, S; Liang, S
作者单位：University of Bonn; Tohoku University
摘要：Let X-i, i epsilon N, be i.i.d. B-valued randorn variables, where B is a real separable Banach space. Let Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z(n) = E(exp(nPhi(Sigma(i=1)(n) X-i/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 16 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z(n) as n --> infinity is given, valid to all ...
