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作者：Nourdin, Ivan; Peccati, Giovanni; Reinert, Gesine
作者单位：Universite Paris Cite; Sorbonne Universite; University of Luxembourg; University of Oxford
摘要：We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the normal and chi-square approximations of any homogenous sum can be completely characterized and assessed by first switching to its Wiener chaos counterpart, and (b) the simple upper bounds and convergence...
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作者：Le Jan, Yves
作者单位：Universite Paris Saclay
摘要：We study the Poissonnian ensembles of Markov loops and the associated renormalized self intersection local times.
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作者：Gubinelli, Massimiliano; Tindel, Samy
作者单位：Universite PSL; Universite Paris-Dauphine; Universite de Lorraine
摘要：We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space-time Gaussian noise with singular space covariance and Brownian time dependence.
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作者：Cerf, R.; Messikh, R. J.
作者单位：Universite Paris Saclay
摘要：We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the size of the box grows fast enough, we establish a large deviation principle that proves the appearance of a round Wulff crystal.
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作者：Barral, Julien; Fournier, Nicolas; Jaffard, Stephane; Seuret, Stephane
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We construct a nondecreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.
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作者：Blanchard, Philippe; Roeckner, Michael; Russo, Francesco
作者单位：University of Bielefeld; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Institut Polytechnique de Paris; ENSTA Paris
摘要：We consider a porous media type equation over all of R-d, d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of...
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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：We prove the almost sure invariance principle for stationary R(d)-valued random processes (with very precise dimension-independent error terms). solely under a strong assumption concerning the characteristic functions of these processes This assumption is easy to check for large classes of dynamical systems or Markov chains using strong or weak spectral perturbation arguments
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作者：Barlow, Martin T.; Masson, Robert
作者单位：University of British Columbia
摘要：Let M(n) be the number of steps of the loop-erasure of a simple random walk on Z(2) from the origin to the circle of radius n. We relate the moments of M(n) to Es(n), the probability that a random walk and an independent loop-erased random walk both started at the origin do not intersect up to leaving the ball of radius n. This allows us to show that there exists C such that for all n and all k = 1,2,..., E[M(n)(k)] <= C(k)k!E[M(n)](k) and hence to establish exponential moment bounds for M(n)....
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作者：Gaertner, J.; den Hollander, F.; Maillard, G.
作者单位：Technical University of Berlin; Leiden University; Leiden University - Excl LUMC; Aix-Marseille Universite
摘要：In this paper we study intermittency for the parabolic Anderson equation partial derivative u/partial derivative t = kappa Delta u + gamma xi u with u:Z(d) x [0, infinity) -> R, where kappa is an element of [0, infinity) is the diffusion constant. Delta is the discrete Laplacian, gamma is an element of (0, infinity) is the coupling constant, and xi : Z(d) x [0, infinity) -> R is a space-time random medium. The solution of this equation describes the evolution of a reactant u under the influenc...
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作者：Chaumont, L.; Doney, R. A.
作者单位：Universite d'Angers; University of Manchester
摘要：We prove that when a sequence of Levy processes X((n)) or a normed sequence of random walks S((n)) converges as on the Skorokhod space toward a. Levy process X. the sequence L((n)) of local times at the supremum of X((n)) converges uniformly on compact sets in probability toward the local time at the supremum of X A consequence of this result is that the sequence of (quadrivariate) ladder processes (both ascending and descending) converges jointly in law toward the ladder processes of X As an ...
