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作者：Ekstrom, Erik; Hobson, David; Janson, Svante; Tysk, Johan
作者单位：Uppsala University; University of Warwick
摘要：Given a centred distribution, can one find a time-homogeneous martingale diffusion starting at zero which has the given law at time 1? We answer the question affirmatively if generalized diffusions are allowed.
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作者：Mikosch, Thomas; Wintenberger, Olivier
作者单位：University of Copenhagen; Universite PSL; Universite Paris-Dauphine
摘要：We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of Nagaev (Theory Probab Appl 14:51-64, 193-208, 1969) and Nagaev (Ann Probab 7:745-789, 1979) for iid regularly varying sequences. The proof uses an idea of Jakubowski (Stoch Proc Appl 44:291-327, 1993; 68:1-20, 1997) in the context of central limit theorems with infinite variance stable limits. We illustrate the principle for stochastic vo...
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作者：Pfander, Goetz E.; Rauhut, Holger; Tropp, Joel A.
作者单位：Constructor University; University of Bonn; California Institute of Technology
摘要：This paper establishes the restricted isometry property for a Gabor system generated by n (2) time-frequency shifts of a random window function in n dimensions. The sth order restricted isometry constant of the associated n x n (2) Gabor synthesis matrix is small provided that s a parts per thousand currency sign c n (2/3) / log(2) n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsity s with respect to n. The proof depend...
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作者：Borodin, Alexei; Gorin, Vadim
作者单位：Massachusetts Institute of Technology (MIT); California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
摘要：Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller Markov process. The dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel. The key idea is to identify random point processes on with q-Gibbs measures on Gelfand-Tsetlin schemes and construct Markov processes...
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作者：Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); Seoul National University (SNU); Kyoto University
摘要：In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.
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作者：Le, V.; Pardoux, E.; Wakolbinger, A.
作者单位：Aix-Marseille Universite; Goethe University Frankfurt
摘要：We obtain a representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. As in the classical Ray-Knight representation, the excursions of H are the exploration paths of the trees of descendants of the ancestors at time t = 0, and the local time of H at height t measures the population size at time t. We cope with the dependence in the r...
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作者：Arguin, Louis-Pierre; Bovier, Anton; Kistler, Nicola
作者单位：Universite de Montreal; University of Bonn
摘要：We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson cluster process, where the positions of the clusters is a Poisson process with intensity measure with exponential density. The law of the individual clusters is characterized as branching Brownian motions conditioned to perform unusually large displacements, and its existence is proved. The proof combines...
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作者：Bordenave, Charles; Guionnet, Alice
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Consider an Hermitian random matrix with, above the diagonal, independent entries with -stable symmetric distribution and . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as goes to infinity. When and , we give vanishing bounds on the -norm of the eigenvectors normalized to have unit -norm. On the contrary, when , we prove that these eigenvectors are localized.
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作者：Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita
作者单位：University of Erlangen Nuremberg; University of Freiburg; University of Duisburg Essen
摘要：The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the individuals in the population at a fixed time. The goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies. We encode the genealogy of the population as an (isometry class of an) ultra-metric space wh...
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作者：Eberle, Andreas; Marinelli, Carlo
作者单位：University of Bonn; Free University of Bozen-Bolzano
摘要：We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications t...
