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作者：Albeverio, Sergio; De Vecchi, Francesco C.; Gubinelli, Massimiliano
作者单位：University of Bonn
摘要：We prove an explicit formula for the law in zero of the solution of a class of elliptic SPDE in R-2. This formula is the simplest instance of dimensional reduction, discovered in the physics literature by Parisi and Sourlas (Phys. Rev. Lett. 43 (1979) 744-745), which links the law of an elliptic SPDE in d + 2 dimension with a Gibbs measure in d dimensions. This phenomenon is similar to the relation between a Rd+1 dimensional parabolic SPDE and its R-d dimensional invariant measure. As such, di...
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作者：Banderier, Cyril; Marchal, Philippe; Wallner, Michael
作者单位：Universite Paris 13; Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux
摘要：Polya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of the time (mod p). We extend the work of Flajolet et al. on Polya urns: the generating function encoding the evolution of the urn is studied by methods of analytic combinatorics. We show that the initial partial differential equations lead to ordinary linear diff...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Saclay
摘要：We consider the model of Brownian motion indexed by the Brownian tree. For every r >= 0 and every connected component of the set of points where Brownian motion is greater than r, we define the boundary size of this component, and we then show that the collection of these boundary sizes evolves when r varies like a well-identified growth-fragmentation process. We then prove that the same growth-fragmentation process appears when slicing a Brownian disk at height r and considering the perimeter...
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作者：Blondel, Oriane; Hilario, Marcelo R.; Teixeira, Augusto
作者单位：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); Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we study random walks on dynamical random environments in 1 + 1 dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a concentration inequality around the asymptotic speed. The mixing hypothesis imposes a polynomial decay rate of covariances on the environment with sufficiently high exponent but does not impose uniform mixing. Examples of environments for which our methods ap...
