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作者：Dekking, Michel; Simon, Karoly; Szekely, Balazs
作者单位：Delft University of Technology; Budapest University of Technology & Economics
摘要：In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson.
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作者：Adams, Stefan; Collevecchio, Andrea; Koenig, Wolfgang
作者单位：University of Warwick; Universita Ca Foscari Venezia; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider N bosons in a box in R-d with volume N/rho under the influence of a mutually repellent pair potential. The particle density p is an element of (0, infinity) is kept fixed. Our main result is the identification of the limiting free energy, f(beta, p), at positive temperature 1/beta, in terms of an explicit variational formula, for any fixed rho if beta is sufficiently small, and for any fixed beta if rho is sufficiently small. The thermodynamic equilibrium is described by the symmet...
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作者：Yilmaz, Atilla
作者单位：University of California System; University of California Berkeley
摘要：We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on Z(d). There exist variational formulae for the quenched and averaged rate functions I(q) and I(a), obtained by Rosenbluth and Varadhan, respectively. I(q) and I(a) are not identically equal. However, when d >= 4 and the walk satisfies the so-called (T) condition of Sznitman, they have been previously shown to be equal on an open set A(eq). For every xi is an element of A(eq), we prove th...
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作者：Baxendale, Peter
作者单位：University of Southern California
摘要：This is a brief survey of T. E. Harris's work on recurrent Markov processes and on stochastic flows, and of some more recent work in these fields.
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作者：Hairer, Martin; Manson, Charles
作者单位：New York University; University of Warwick
摘要：We consider a diffusion process with coefficients that are periodic outside of an interface region of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under diffusive resealing. It is clear that outside of the interface, the limiting process must behave like Brownian motion, with diffusion matrices given by the standard theory of homogenization. The interesting behavior therefore occurs on the interface. Our main resul...
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作者：Chaumont, Loic; Uribe Bravo, Geronimo
作者单位：Universite d'Angers; Universidad Nacional Autonoma de Mexico
摘要：A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the state space of the process. In the context of Feller processes with continuous transition densities, we construct by weak convergence considerations the only versions of Markovian bridges which are weakly continuous with respect to their parameter. We use this w...
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作者：Athreya, K. B.; Ney, P. E.
作者单位：Iowa State University; Iowa State University; Indian Institute of Science (IISC) - Bangalore; University of Wisconsin System; University of Wisconsin Madison
摘要：T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book The Theory of Branching Processes, published in 1963.
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作者：Chen, Lung-Chi; Sakai, Akira
作者单位：Fu Jen Catholic University; Hokkaido University
摘要：We consider random walk and self-avoiding walk whose 1-step distribution is given by D, and oriented percolation whose bond-occupation probability is proportional to D. Suppose that D(x) decays as vertical bar x vertical bar(-d-alpha) with alpha > 0. For random walk in any dimension d and for self-avoiding walk and critical/subcritical oriented percolation above the common upper-critical dimension d(c) equivalent to 2(alpha boolean AND 2), we prove large-t asymptotics of the gyration radius, w...
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作者：Pekoez, Erol A.; Roellin, Adrian
作者单位：Boston University; National University of Singapore
摘要：We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of Renyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the exponential asymptotic behavior of a critical Galton Watson process co...
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作者：Liggett, Thomas M.
作者单位：University of California System; University of California Los Angeles
摘要：Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye view of his work in these fields, and of its impact on later research in probability theory and mathematical physics.
