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作者：Liu, Yuan
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (LSI for short). The aim of this paper is threefold: (1) To prove the equivalence of and the Lyapunov condition, which gives a new characterization inspired by Cattiaux et al. (Probab Theory Relat Fields 148(1-2):285-304, 2010). (2) To prove the stability of under bounded perturbations, which gives a transference principle in the sense of Holley-Stro...
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作者：[Anonymous]
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作者：Beltran, J.; Jara, M.; Landim, C.
作者单位：Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it attains it, and that, after hitting the boundary, it performs a diffusion on a lower dimensional simplex, similar to the original one. We also prove that in the diffusive time scale condensing zero-range processes evolve as this absorbed diffusion.
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作者：Le Gouic, Thibaut; Loubes, Jean-Michel
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Based on the Fr,chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the probability measures or of a growing set of probability measures.
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作者：Dahmer, Iulia; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman coalescent and its asymptotic behaviour when the number of leaves of the tree tends to infinity. We show that on the time-scale of the Moran model slowed down by a factor equal to the population size, the (centred and rescaled) external length process converges to a...
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作者：Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider the local eigenvalue distribution of large self-adjoint random matrices with centered independent entries. In contrast to previous works the matrix of variances is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, , converges to a diagonal matrix, , ...
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作者：Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael
作者单位：University of Pisa; Max Planck Society; Technical University of Berlin
摘要：We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point. As a result, synchronization by noise is proven for a large class of SDE with...
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作者：Miller, Jason; Sousi, Perla
作者单位：University of Cambridge
摘要：Suppose that X is a simple random walk on for and, for each t, we let consist of those which have not been visited by X by time t. Let be the expected amount of time that it takes for X to visit every site of . We show that there exists and a time as such that the following is true. For (resp. ), the total variation distance between the law of and the law of i.i.d. Bernoulli random variables indexed by with success probability tends to 0 (resp. 1) as . Let be the first time t that . We also sh...
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作者：Rodriguez, Pierre-Francois
作者单位：University of California System; University of California Los Angeles
摘要：We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h. The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold for percolation, a second parameter characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 p...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
摘要：We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker's position, we are able to prove secon...
