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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：Berkes, Istvan; Hormann, Siegfried; Schauer, Johannes
作者单位：Graz University of Technology; Universite Libre de Bruxelles
摘要：The results of Komlos, Major and Tusnady give optimal Wiener approximation of partial sums of i.i.d. random variables and provide an extremely powerful tool in probability and statistical inference. Recently Wu [Ann. Probab. 35 (2007) 2294-2320] obtained Wiener approximation of a class of dependent stationary processes with finite pth moments, 2 < p <= 4, with error term o(n(1/p)(log n)(gamma)), gamma > 0, and Liu and Lin [Stochastic Process. Appl. 119 (2009) 249-280] removed the logarithmic f...
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作者：Lawler, Gregory F.; Sheffield, Scott
作者单位：University of Chicago; University of Chicago; Massachusetts Institute of Technology (MIT)
摘要：The Schramm-Loewner evolution (SLE kappa) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When kappa < 8, an instance of SLE kappa is a random planar curve with almost sure Hausdorff dimension d = 1 + kappa/8 < 2. This curve is conventionally parametrized by its half plane capacity, rather than by any measure of its d-dimensional volume. For kappa < 8, we use a Doob-Meyer decomposition to construct the unique (under mild assumptions) Markovi...
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作者：Kozma, Gady
作者单位：Weizmann Institute of Science
摘要：We show that critical percolation on a product of two regular trees of degree >= 3 satisfies the triangle condition. The proof does not examine the degrees of vertices and is not perturbative in any sense. It relies on an unpublished lemma of Oded Schramm.
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作者：Li, Xue-Mei; Scheutzow, Michael
作者单位：University of Warwick; Technical University of Berlin
摘要：It is well known that a stochastic differential equation (SDE) on a Euclidean space driven by a Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. When the coefficients are only locally Lipschitz, then a maximal continuous flow still exists but explosion in finite time may occur. If, in addition, the coefficients grow at most linearly, then this flow has the property that for each fixed initial condition x, the solution exists for all times almost surely...
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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：Lalley, Steven P.; Zheng, Xinghua
作者单位：University of Chicago; Hong Kong University of Science & Technology
摘要：Consider a critical nearest-neighbor branching random walk on the d-dimensional integer lattice initiated by a single particle at the origin. Let G(n) be the event that the branching random walk survives to generation n. We obtain the following limit theorems, conditional on the event G(n), for a variety of occupation statistics: ( I) Let V-n be the maximal number of particles at a single site at time n. If the offspring distribution has finite alpha th moment for some integer alpha >= 2, then...
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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：Le Gall, Jean-Francois; Miermont, Gregory
作者单位：Universite Paris Saclay
摘要：We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index alpha is an element of (1, 2). When the number n of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process, which can be constructed from a centered stable process with no negative ju...
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作者：Burdzy, Krzysztof; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We study Markov processes where the time parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other directed path. If two directed paths do not interact, in a suitable sense, then the distributions of the processes on the two paths are conditionally independent, given their values at the common endpoint of the two paths. Conditions on graphs that support suc...
