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作者：Ben Arous, Gerard; Cabezas, Manuel; Cerny, Jiri; Royfman, Roman
作者单位：New York University; University of Vienna
摘要：We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on Z. These scaling limits include the well-known fractional kinetics process, the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call spatially subordinated Brownian motions. We give sufficient conditions for convergence and illustrate these on two important examples.
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作者：Le Gall, Jean-Francois; Lin, Shen
作者单位：Universite Paris Saclay
摘要：We study the range R-n, of a random walk on the d-dimensional lattice Z(d) indexed by a random tree with n vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension d <= 3 that n(-d/4)R(n) converges in distribution to the Lebesgue measure of the support of the integrated super-Brownian excursion (ISE). An auxiliary result shows that the suitably rescaled local times of the tree-indexed random walk converge in distribution to the densit...
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作者：Carmona, Rene; Delarue, Francois
作者单位：Princeton University; Universite Cote d'Azur
摘要：The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of McKean Vlasov type. Motivated by the recent interest in mean-field games, we highlight the connection and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for existence of an optimal control. We also provide examples for which our sufficient conditions for existenc...
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作者：Mytnik, Leonid; Wachtel, Vitali
作者单位：Technion Israel Institute of Technology; University of Munich
摘要：We show that density functions of a (alpha, 1, beta)-superprocesses are almost sure multifractal for alpha > beta + 1, beta is an element of (0, 1) and calculate the corresponding spectrum of singularities.
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作者：Barral, Julien; Kupiainen, Antti; Nikula, Miika; Saksman, Eero; Webb, Christian
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; University of Helsinki
摘要：We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show ...
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作者：Pitman, Jim; Winkel, Matthias
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：Some, but not all processes of the form M-t = exp(-xi(t)) for a pure-jump subordinator xi with Laplace exponent Phi arise as residual mass processes of particle 1 (tagged particle) in Bertoin's partition-valued exchangeable fragmentation processes. We introduce the notion of a Markovian embedding of M = (M-t, t >= 0) in a fragmentation process, and we show that for each Phi, there is a unique (in distribution) binary fragmentation process in which M has a Markovian embedding. The identificatio...
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作者：Gouezel, Sebastien
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is known since the work of Ancona and Gouezel-Lalley that the Martin boundary coincides with the geometric boundary. The goal of this paper is to weaken the finite support assumption. We first show that, in any nonamenable group, there exist probability measures...
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作者：Cox, A. M. G.; Peskir, G.
作者单位：University of Bath; University of Manchester
摘要：We present a constructive probabilistic proof of the fact that if B = (B-t)(t >= 0) is standard Brownian motion started at 0, and mu is a given probability measure on R such that mu({0}) = 0, then there exists a unique left-continuous increasing function b: (0, infinity) -> R boolean OR {+infinity} and a unique left-continuous decreasing function c: (0, infinity) -> R boolean OR (-infinity) such that B stopped at tau(b,c) = inf{t > 0 vertical bar B-t >= b(t) or B-t <= c(t)} has the law p,. The...
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作者：Benjamini, Itai; Duminil-Copin, Hugo; Kozma, Gady; Yadin, Ariel
作者单位：Weizmann Institute of Science; University of Geneva; Ben-Gurion University of the Negev
摘要：We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on Z(d). We prove that the vector space of harmonic functions growing at most linearly is (d + 1)-dimensional almost surely. Further, there are no nonconstant sublinear harmonic functions (thus implying the uniqueness of the corrector). A main ingredient of the proof is a quantitative, annealed version of the Avez entropy argument. This also provides boun...
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作者：Cerf, Raphael
作者单位：Universite Paris Saclay
摘要：We consider the standard site percolation model on the d-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the two-arms exponent is larger than or equal to 1/2. We improve slightly this lower bound in any dimension d >= 2. Next, starting only with the hypothesis that theta(p) > 0, without using the slab technology, we derive a quantitative estimate establishing long-rang...
