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作者：Ricard, Eric; Xu, Quanhua
作者单位：Universite de Caen Normandie; Wuhan University; Universite Marie et Louis Pasteur
摘要：Let M be a von Neumann algebra equipped with a faithful semifinite normal weight phi and N be a von Neumann subalgebra of M such that the restriction of phi to N is semifinite and such that N is invariant by the modular group of phi. Let epsilon be the weight preserving conditional expectation from M onto N. We prove the following inequality: parallel to x parallel to(2)(p) >= parallel to epsilon(x)parallel to(2)(p) + (p - 1)parallel to x - epsilon(x)parallel to(2)(p), x is an element of L-p(M...
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作者：Azmoodeh, Ehsan; Malicet, Dominique; Mijoule, Guillaume; Poly, Guillaume
作者单位：University of Luxembourg; Universite Paris Saclay; Universite de Rennes
摘要：The celebrated Nualart-Peccati criterion [Ann. Probab. 33 (2005) 177-193] ensures the convergence in distribution toward a standard Gaussian random variable N of a given sequence {X-n}(n >= 1) of multiple Wiener-Ito integrals of fixed order, if E[X-n(2)] -> 1 and E[X-n(4)] -> E[N-4] = 3. Since its appearance in 2005, the natural question of ascertaining which other moments can replace the fourth moment in the above criterion has remained entirely open. Based on the technique recently introduce...
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作者：Fontbona, Joaquin; Jourdain, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Inria
摘要：The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale. In the case of (not necessarily reversible) Markov diffusion processes, we use Girsanov theory to explicit the Doob-Meyer decomposition of this submartingale. We deduce a stochastic analogue of the well-known entropy dissipation formula, which is valid for g...
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we give a very accurate description of the way the simple exclusion process relaxes to equilibrium. Let P-t denote the semi-group associated the exclusion on the circle with 2N sites and N particles. For any initial condition chi, and for any t >= 4N(2)/9 pi(2) log N, we show that the probability density P-t (chi, center dot) is given by an exponential tilt of the equilibrium measure by the main eigenfunction of the particle system. As 4N(2)/9 pi(2) log N is smaller than the mix...
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作者：Cebron, Guillaume
作者单位：Saarland University
摘要：This paper investigates homomorphisms a la Bercovici-Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with measures on the space of Hermitian matrices and on the unitary group. The previous results combined with a matricial model of Benaych-Georges and Cabanal-Duvillard allow us to define and study the large N limit of a new matricial model on the unitary group for free multiplicative Levy processes.
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作者：Garban, Christophe; Rhodes, Remi; Vargas, Vincent
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; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We construct a stochastic process, called the Liouville Brownian motion, which is the Brownian motion associated to the metric e(gamma X(z)) dz(2), gamma < gamma(c) = 2 and X is a Gaussian Free Field. Such a process is conjectured to be related to the scaling limit of random walks on large planar maps eventually weighted by a model of statistical physics which are embedded in the Euclidean plane or in the sphere in a conformal manner. The construction amounts to changing the speed of a standar...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for the parabolic Anderson equation {partial derivative u/partial derivative t (t, x) = 1/2 Delta u(t, x) + V (t, x)u(t, x), u(0, x) = u(0)(x), where the homogeneous generalized Gaussian noise V (t, x) is, among other forms, white or fractional white ...
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作者：Kolb, Martin; Savov, Mladen
作者单位：University of Paderborn; Bulgarian Academy of Sciences
摘要：In this paper, we study the behavior of Brownian motion conditioned on the event that its local time at zero stays below a given increasing function f up to time T. For a class of nonincreasing functions f, we show that the conditioned process converges, as T -> infinity, to a limit process and we derive necessary and sufficient conditions for the limit to be transient. In the transient case, the limit process is described explicitly, and in the recurrent case we quantify the entropic repulsio...
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作者：Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We construct a conformal welding of two Lionville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE), thereby resolving a variant of a conjecture of Peter Jones. We also demonstrate some surprising symmetries of this construction, which are consistent with the belief that (path-decorated) random planar maps have (SLE-decorated) Liouville quantum gravity as a scaling limit. We present several precise conj...
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作者：Cerrai, Sandra; Salins, Michael
作者单位：University System of Maryland; University of Maryland College Park
摘要：In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski Kramers approximation is not only valid for small time, but in the zero noise limi...
