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作者：Ferrari, Pablo A.; Martin, James B.; Pimentel, Leandro P. R.
作者单位：Universidade de Sao Paulo; University of Oxford; Delft University of Technology
摘要：We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle theta of the cone: for theta >= 180 degrees, the direction is deterministic, while for theta < 180 degrees, it is random, and its distribution can be given explicitly in certain cases. We als...
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作者：Jacobsen, Martin; Mikosch, Thomas; Rosinski, Jan; Samorodnitsky, Gennady
作者单位：University of Copenhagen; University of Copenhagen; University of Tennessee System; University of Tennessee Knoxville; Cornell University
摘要：In this paper, we consider certain sigma-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have regularly varying tails as well. This turns out to be related to the presence of a particular cancellation property in sigma-finite measures, which in turn, is related to the uniqueness of the solution of certain functional equations. The techniques we develop are...
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作者：Craddock, Mark; Lennox, Kelly A.
作者单位：University of Technology Sydney
摘要：This paper uses Lie symmetry methods to calculate certain expectations for a large class of Ito diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form E-x(e(-lambda Xt-f0tg(Xs)ds)) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for whic...
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作者：Garnier, Josselin; Solna, Knut
作者单位：Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; University of California System; University of California Irvine
摘要：In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schrodinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation ...
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作者：Buchmann, Boris; Chan, Ngai Hang
作者单位：Monash University; Chinese University of Hong Kong
摘要：Consider Z(t)(f) (u) = integral o(tu) f (N(s)) ds, t > 0, u is an element of [0, 1], where N = (N(t))t is an element of R is a normal process and f is a measurable real-valued function satisfying Ef(N(0))(2) < infinity and Ef (N(0)) = 0. If the dependence is sufficiently weak Hariz [J. Multivariate Anal. 80 (2002) 191-216] showed that Z(t)(f)/t(1/2) converges in distribution to a multiple of standard Brownian motion as t -> infinity. If the dependence is sufficiently strong, then Zt/(EZ(t) (1)...
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作者：D'Angeli, Daniele; Donno, Alfredo
作者单位：University of Geneva
摘要：In this work we define two kinds of crested product for reversible Markov chains, which naturally appear as a generalization of the case of crossed and nested product, as in association schemes theory, even if we do a construction that seems to be more general and simple. Although the crossed and nested product are inspired by the study of Gelfand pairs associated with the direct and the wreath product of two groups, the crested products are a more general construction, independent from the Ge...
