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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：Shcherbina, T.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices , where A (m,n) is a m x n complex random matrix with independent and identically distributed entries and . We show that for the correlation function of any even order the asymptotic behavior in the bulk and at the edge of the spectrum coincides with those for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common pr...
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作者：Xiao, Yimin; Zheng, Xinghua
作者单位：Michigan State University; Hong Kong University of Science & Technology
摘要：Let be a continuous time random walk in an environment of i.i.d. random conductances , where E (d) is the set of nonoriented nearest neighbor bonds on the Euclidean lattice and d a parts per thousand yen 3. Let be the range of X. It is proved that, for almost every realization of the environment, dim(H) R = dim(P) R = 2 almost surely, where dim(H) and dim(P) denote, respectively, the discrete Hausdorff and packing dimension. Furthermore, given any set , a criterion for A to be hit by X (t) for...
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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：Arguin, Louis-Pierre; Chatterjee, Sourav
作者单位：Universite de Montreal; New York University
摘要：Random overlap structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits of Gibbs measures under the appropriate algebra of functions. We prove that the so called 'cavity mapping' on the space of ROSt's is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spi...
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作者：Croydon, D. A.; Fribergh, A.; Kumagai, T.
作者单位：University of Warwick; New York University; Kyoto University
摘要：We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs.
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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...
