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作者：Yadin, Ariel; Yehudayoff, Amir
作者单位：University of Cambridge; Technion Israel Institute of Technology
摘要：Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z(2) is SLE(2). We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another). We show that if the scaling limit of the random walk is planar Brownian motion, then the scaling limit of its loop-erasure is SLE(2). Our main contribution is showing that for such graphs, the discrete Poisson kernel can be approximated by ...
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作者：Castell, Fabienne; Guillotin-Plantard, Nadine; Pene, Francoise; Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Random walks in random scenery are processes defined by Z(n) := Sigma(n)(k) = 1 X-xi(1)+... + X-k, where (X-k, k >= 1) and (xi(y), y is an element of Z) are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index alpha is an element of (0, 2] and beta is an element of (0, 2], respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved the convergence in distrib...
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作者：Curien, Nicolas; Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those chords that do not intersect the previous ones. After throwing infinitely many chords and taking the closure of the resulting set, one gets a random compact subset of the unit disk whose complement is a countable union of triangles. We show that this limiting ...
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作者：Kurtz, Thomas G.; Rodrigues, Eliane R.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Universidad Nacional Autonoma de Mexico
摘要：Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a level, but unlike earlier constructions, the levels change with time. In fact, death of a particle occurs only when the level of the particle crosses a specified level r, or for the limiting models, hits infinity. For branching Markov processes, at each time t conditio...
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作者：Kuznetsov, Alexey
作者单位：York University - Canada
摘要：We study the Wiener-Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener-Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite series representations and asymptotic expansions for the density of supremum, explicit expressions for the Wiener-Hopf factors and the Mellin transform of the supremum, quasi-periodicity and functional identities for these functions, finite produc...
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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：Sheffield, Scott; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Microsoft
摘要：Gerard Watts predicted a formula for the probability in percolation that there is both a left-right and an up-down crossing, which was later proved by Julien Dubedat. Here we present a simpler proof due to Oded Schramm, which builds on Cardy's formula in a conceptually appealing way: the triple derivative of Cardy's formula is the sum of two multi-arm densities. The relative sizes of the two terms are computed with Girsanov conditioning. The triple integral of one of the terms is equivalent to...
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作者：Morvai, Gusztav; Weiss, Benjamin
作者单位：MTA-BME Stochastics Research Group; Hebrew University of Jerusalem
摘要：We study the problem of finding an universal estimation scheme h(n) : R(n) -> R, n = 1, 2,... which will satisfy limt(->infinity) l/t Sigma(t)(i=1)|h(i)(X(0), X(1)....,X(i-l)) -E(X(i)|X(0), X(1),....,X(i-1))|(p) = 0 a.s. for all real valued stationary and ergodic processes that are in L. We will construct a single such scheme for all 1 < p <= infinity, and show that for p = 1 mere integrability does not suffice but L log(+) L does.
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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：Garban, Christophe
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：We survey in this paper the main contributions of Oded Schramm related to noise sensitivity. We will describe in particular his various works which focused on the spectral analysis of critical percolation (and more generally of Boolean functions), his work on the shape-fluctuations of first passage percolation and finally his contributions to the model of dynamical percolation.
