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作者：Benjamini, I; Pemantle, R; Peres, Y
作者单位：Weizmann Institute of Science; University of Wisconsin System; University of Wisconsin Madison; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：We construct a nearest-neighbor process {S-n} on Z that is less predictable than simple random walk, in the sense that given the process until time n, the conditional probability that Sn+k = x is uniformly bounded by Ck(-alpha) for some alpha > 1/2. From this process, we obtain a probability measure mu on oriented paths in Z(3) such that the number of intersections of two paths, chosen independently according to mu, has an exponential tail. (For d greater than or equal to 4, the uniform measur...
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作者：Salzano, M; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：We provide a new proof, substantially simpler than Zhang's original one, that for the contact process on homogeneous trees, local survival implies complete convergence.
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作者：Lee, TY; Torcaso, F
作者单位：University System of Maryland; University of Maryland College Park
摘要：We extend a result of Freidlin and Gartner for KPP wave fronts to the case d greater than or equal to 2 for i.i.d. random media. We show a wave front propagation speed is attained for the discrete-space (lattice) KPP using a large deviation approach.
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作者：Seppalainen, T
作者单位：Iowa State University
摘要：We derive the limiting shape for the following model of first-passage bond percolation on the two-dimensional integer lattice: the percolation is directed in the sense that admissible paths are nondecreasing in both coordinate directions. The passage times of horizontal bonds are Bernoulli distributed, while the passage times of vertical bonds are all equal to a deterministic constant. To analyze the percolation model, we couple it with a one-dimensional interacting particle system. This parti...
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作者：Shieh, NR
作者单位：National Taiwan University
摘要：Let X be a symmetric Levy process in R-d, d = 2, 3. We assume that X has independent alpha(j)-stable components, 1 < alpha(d) less than or equal to ... less than or equal to alpha(1) < 2 (a process with stable components, by Pruitt and Taylor), or more generally that X is d-dimensionally self-similar with similarity exponents H-j, H-j = 1/alpha(j) (a dilation-stable process, by Kunita). Let a given integer k greater than or equal to 2 be such that k(H - 1) < H, H = Sigma(j=1)(d) H-j. We prove ...
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作者：Seppalainen, T
作者单位：Iowa State University
摘要：We study translation-invariant random-cluster measures with techniques from large deviation theory and convex analysis. In particular, we prove a large deviation principle with rate function given by a specific entropy, and a Dobrushin-Lanford-Ruelle variational principle that characterizes translation-invariant random-cluster measures as the solutions of the variational equation for free energy. Consequences of these theorems include inequalities for edge and cluster densities of translation-...
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作者：Wuthrich, MV
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider d-dimensional Brownian motion in a truncated Poissonian potential conditioned to reach a remote location. If Brownian motion starts at the origin and ends in an hyperplane at distance L from the origin, the transverse fluctuation of the path is expected to be of order L-xi. We are interested in a lower bound for xi. We first show that xi greater than or equal to 1/2 in dimensions d greater than or equal to 2 and then we prove superdiffusive behavior for d = 2, resulting in xi great...
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作者：Klenke, A
作者单位：University of Erlangen Nuremberg
摘要：We consider two spatial branching models on R-d: branching Brownian motion with a branching law in the domain of normal attraction of a (1 + beta) stable law, 0 < beta less than or equal to 1, and the corresponding high density limit measure valued diffusion. The longtime behavior of both models depends highly on beta and d. We show that for d less than or equal to 2/beta the only invariant measure is delta(0), the unit mass on the empty configuration. Furthermore, we give a precise condition ...
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作者：Gantert, N
作者单位：Technical University of Berlin
摘要：For an i.i.d. sequence of random variables with a semiexponential distribution, we give a functional form of the Erdos-Renyi law for partial sums. In contrast to the classical case, that is, the case where the random variables have exponential moments of all orders, the set of limit points is not a subset elf the continuous functions. This reflects the bigger influence of extreme values. The proof is based on a large deviation principle for the trajectories of the corresponding random walk. Th...
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作者：Enchev, OB
作者单位：Boston University
摘要：Given a Riemannian manifold M and loop phi: S-1 bar right arrow M, we construct a Gaussian random process S-1 There Exists theta curved right arrow X-theta epsilon T-phi(theta)M, which is an analog of the Brownian motion process in the sense that the formal covariant derivative theta curved right arrow del(theta)X(theta) appears as a stationary process whose spectral measure is uniformly distributed over some discrete set. We show that X satisfies the two-point Markov property (reciprocal proc...
