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作者：Budhiraja, Amarjit; Dupuis, Paul; Ganguly, Arnab
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; University of Louisville
摘要：Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive functionals of a PRM.
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作者：Hachem, Walid; Hardy, Adrien; Najim, Jamal
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Royal Institute of Technology; Universite Gustave-Eiffel; ESIEE Paris; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which converges almost surely toward that edge and fluctuates according to the Tracy-Widom law at the scale N...
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Given a simply connected planar domain D, distinct points x, y is an element of partial derivative D, and kappa > 0, the Schramm-Loewner evolution SLE kappa is a random continuous non-self-crossing path in (D) over bar from x to y. The SLE kappa (rho(1); rho(2)) processes, defined for rho(1), rho(2) > -2, are in some sense the most natural generalizations of SLE kappa. When kappa <= 4, we prove that the law of the time-reversal of an SLE kappa (rho(1); rho(2)) from x to y is, up to parameteriz...
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作者：Kious, Daniel
摘要：In this paper, we work on a class of self-interacting nearest neighbor random walks, introduced in [Probab. Theory Related Fields 154 (2012) 149-163], for which there is competition between repulsion of neighboring edges and attraction of next-to-neighboring edges. Erschler, Toth and Werner proved in [Probab. Theory Related Fields 154 (2012) 149-163] that, for any L >= 1, if the parameter alpha belongs to a certain interval (alpha(L+1), alpha(L)), then such random walks localize on L + 2 sites...
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作者：Rossignol, Raphael
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem f...
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作者：Ziliotto, Bruno
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole
摘要：Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guarantee the asymptotic value. We disprove these two long-standing conjectures by providing an example of ...
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作者：Li, Xue-Mei
作者单位：University of Warwick
摘要：We study random perturbation to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm 1. We prove that the projections of the solutions to the perturbed equations, converge, after suitable resealing, to a Brownian motion scaled by 8/n(n-1) where n is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal ...
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作者：Rudelson, Mark; Samorodnitsky, Alex; Zeitouni, Ofer
作者单位：University of Michigan System; University of Michigan; Hebrew University of Jerusalem; Weizmann Institute of Science; New York University
摘要：We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok's estimator gives a polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect ma...
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作者：Da Prato, G.; Flandoli, F.; Rockner, M.; Veretennikov, A. Yu.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Bielefeld; University of Leeds; HSE University (National Research University Higher School of Economics); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the sub-differential of a convex function and a bounded part. This generalizes a classical result by one of the authors to infinite dimensions. Our results also generalize and improve recent results by N. Champagnat and P. E. Jabin, proved in finite dimensions, in the case where their diffusion matrix is constant and nond...
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作者：Ren, Jiagang; Wu, Jing
作者单位：Sun Yat Sen University
摘要：In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Sole's idea, we characterize in Holder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of ...
