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作者：Dalang, Robert C.; Mueller, Carl
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester
摘要：It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases where (k - 1)d = 2kN, there are a.s. no k-multiple points.
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作者：Geiss, Stefan; Toivola, Anni
作者单位：University of Jyvaskyla; University of Innsbruck
摘要：We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in L-p for 2 <= p < infinity for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.
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作者：Kiss, Demeter; Manolescu, Ioan; Sidoravicius, Vladas
作者单位：University of Cambridge; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Self-destructive percolation with parameters p, delta is obtained by taking a site percolation configuration with parameter p, closing all sites belonging to infinite clusters, then opening every closed site with probability delta, independently of the rest. Call theta (p, delta) the probability that the origin is in an infinite cluster in the configuration thus obtained. For two-dimensional lattices, we show the existence of delta > 0 such that, for any p > p(c), theta (p, delta) = 0. This pr...
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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：Denisov, Denis; Wachtel, Vitali
作者单位：University of Manchester; University of Munich
摘要：We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Browni...
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作者：Chen, Le; Dalang, Robert C.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but this measure may also have noncompact support and even be nontempered (e.g., with exponentially growing tails). Existence and uniqueness of a random field solution is proved without appealing to Gronwall's lemma, by keeping tight control over m...
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作者：Lubetzky, Eyal; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes Etudes Sci. Publ. Math. 90 (1999) 5-43], it was there shown to be governed by the first level of Fourier coefficients in the central case of monotone functions at a constant critical probability p(c). Here we study noise sensitivity and a natural stronger version of it, addressing the effect of noise gi...
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作者：Gravner, Janko; Holroyd, Alexander E.
作者单位：University of California System; University of California Davis; Microsoft
摘要：We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random initial seed on an interval of length L, with probability tending to one as L -> infinity, the evolution is a replicator. That is, a region of space time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of oth...
