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作者：Járai, AA
作者单位：University of British Columbia
摘要：We study several kinds of large critical percolation clusters in two dimensions. We show that from the microscopic (lattice scale) perspective these clusters can be described by Kesten's incipient infinite cluster (IIC), as was conjectured by Aizenman. More specifically, we establish this for incipient spanning clusters, large clusters in a finite box and the inhomogeneous model of Chayes, Chayes and Durrett. Our results prove the equivalence of several natural definitions of the IIC. We also ...
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作者：Lyons, R; Permantle, R
作者单位：Indiana University System; Indiana University Bloomington; University System of Georgia; Georgia Institute of Technology; University System of Ohio; Ohio State University
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作者：Jacka, S; Tribe, R
作者单位：University of Warwick
摘要：This paper considers some measure-valued processes {X-t:t is an element of [0, T]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Phi of the process are given that imply that the expectations E(Phi(X-T)) are comparable to the constant branching case. Applications to hitting estimates and regularity of solutions are discussed. The resul...
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作者：Harrelson, D; Houdré, C
作者单位：Hope College; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
摘要：m-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Levy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by m-dependent ones is the...
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作者：Prabhakar, B
作者单位：Stanford University; Stanford University
摘要：We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean tau > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as I. Assuming that such a fixed point...
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作者：Csörgö, M; Szyszkowicz, B; Wang, QY
作者单位：Carleton University; Australian National University
摘要：Let X, X-1, X-2,... be a sequence of nondegenerate i.i.d. random variables with zero means. In this paper we show that a self-normalized version of Donsker's theorem holds only under the assumption that X belongs to the domain of attraction of the normal law. A thus resulting extension of the arc sine law is also discussed. We also establish that a weak invariance principle holds true for self-normalized, self-randomized partial sums processes of independent random variables that are assumed t...
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作者：Marckert, JF; Mokkadem, A
作者单位：Universite Paris Saclay
摘要：In this paper, we show a strong relation between the depth first processes associated to Galton-Watson trees with finite variance, conditioned by the total progeny: the depth first walk, the depth first queue process, the height process; a consequence is that these processes (suitably normalized) converge to the same Brownian excursion. This provides an alternative proof of Aldous' one of the convergence of the depth first walk to the Brownian excursion which does not use the existence of a li...
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作者：Steele, JM; Zhang, Y
作者单位：University of Pennsylvania; University of Colorado System; University of Colorado at Colorado Springs
摘要：We study the paths of minimal cost for first-passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these. This inequality permits us to answer a long-standing question of Hammersley and Welsh on the shift differentiability of the time constant. Specifically, we show that for subcritical Bernoulli percolation the time constant is not shift differentiable when p is close to one-half.
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作者：Alabert, A; Ferrante, M
作者单位：Autonomous University of Barcelona; University of Padua
摘要：We consider linear nth order stochastic differential equations on [0, 1], with linear boundary conditions supported by a finite subset of [0, 1]. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.
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作者：Owhadi, H
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations dy(t) = domega(t) - delV(y(t))dt, y(0) = 0. When d = 1 and V is not periodic but obtained as a superposition of an infinite number of periodic potentials with geometrically increasing periods [V(x) = Sigma(k=0)(infinity) U-k(x/R-k), where U-k are smooth functions of period 1, U-k(0) = 0, and R-k grows exponentially fast with k] we can show that yt has an anomalous slow behavior and we obtain ...
