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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; Polytechnic University of Milan
摘要：We study quasi-stationary measures for conservative particle systems in the infinite lattice. Existence of quasi-stationary measures is established for a fairly general class of reversible systems. For the special cases of a system of independent random walks and the symmetric simple exclusion process, it is shown that qualitative features of quasi-stationary measures change drastically with dimension.
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作者：Bolthausen, E; Deuschel, JD; Giacomin, G
作者单位：University of Zurich; Technical University of Berlin; Universite Paris Cite
摘要：We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surface in the presence of a hard wall. The basic ingredient of the proof is the analysis of the maximum of the field which requires a multiscale analysis reducing the problem essentially to a problem on a field with a tree structure.
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作者：Pinsky, RG
作者单位：Technion Israel Institute of Technology
摘要：We investigate the set of invariant probability distributions for measure-valued diffusion processes corresponding to semilinear operators of the form u(t) = L(0)u+betau-alphau(2), where L-0 = (1/2) Sigma(i)(,j=1)(d) alpha(i,j) alpha(2)/alphax(i)alphax(j) + Sigma(i)(= 1)(d) b(i) alpha/alphax(i).
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作者：Zerner, MPW; Merkl, F
作者单位：Stanford University; University of Bielefeld; Technion Israel Institute of Technology
摘要：We solve the problem posed by S. A. Kalikow whether the event that the x-coordinate of a random walk in a two-dimensional random environment approaches infinity has necessarily probability either zero or one. The answer is yes if we assume the environment to be i.i.d. and in general no if we allow the environment to be just stationary and ergodic.
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作者：Maaoula, F
作者单位：Universite de Tunis-El-Manar; Faculte des Sciences de Tunis (FST)
摘要：We extend the almost-sure central limit theorem to martingale additive functionals of a recurrent Markov process. In the particular case of positive recurrence, we also derive two invariance principles similar to the central limit theorem and the law of the iterated logarithm.
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作者：Levin, DA; Pemantle, R; Peres, Y
作者单位：University of Connecticut; University of Wisconsin System; University of Wisconsin Madison; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：Suppose that a coin with bias 9 is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let we be the distribution of the observed sequence of coin tosses, and let u(n) denote the chance of a renewal at time n. Harris and Keane showed that if Sigma(n=1)(infinity) u(n)(2)=infinity, then u(theta) and u(0) are singular, while if Sigma(n=1)(infinity) u(n)(2) < infinity and theta is small enough, then u(theta) is absolutely continuous with respect to go. They ...
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作者：Pemantle, R; Stacey, AM
作者单位：University System of Ohio; Ohio State University; University of Cambridge
摘要：We show that the branching random walk on a Galton-Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton-Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded deg...
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作者：Allouba, H; Zheng, W
作者单位：Indiana University System; Indiana University Bloomington; East China Normal University; University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst
摘要：We introduce a class of interesting stochastic processes based on Brownian-time processes. These are obtained by taking Markov processes and replacing the time parameter with the modulus of Brownian motion. They generalize the iterated Brownian motion (IBM) of Burdzy and the Markov snake of Le Gall, and they introduce new interesting examples. After defining Brownian-time processes, we relate them to fourth order parabolic partial differential equations (PDE's). We then study their exit proble...
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作者：Brzezniak, Z; Peszat, S
作者单位：University of Hull; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：The existence of a martingale solution to 2-dimensional stochastic Euler equations is proved. The constructed solution is a limit as the viscosity converges to zero of a sequence of solutions to modified Navier-Stokes equations.
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作者：Marchal, P
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We define a class of processes on the boundary of a regular tree that can be viewed as stable Levy processes on (Z/n(0)Z)(N). We show that the range of these processes can be compared with a Bernoulli percolation as in Peres which easily leads to various results on the intersection properties. We develop an alternative approach based on the comparison with a branching random walk. By this method we establish the existence of points of infinite multiplicity when the index of the process equals ...
