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作者：Marckert, Jean-Francois; Miermont, Gregory
作者单位：Universite de Bordeaux; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend, up to scaling factors, on details of the class of maps that are sampled. Previous works on the topic, starting with Chassaing and Schaeffer, have shown that the radius of a random quadrangulation with n faces, that...
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作者：van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L.
作者单位：Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
摘要：In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an H-cylindrical Brownian motion. Our approach is based on a two-sided L-p-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of L(H, E)-valued functions introduced recently by two of the...
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作者：Panchenko, Dmitry; Talagrand, Michel
作者单位：Massachusetts Institute of Technology (MIT); Sorbonne Universite; University System of Ohio; Ohio State University
摘要：In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with constrained overlaps. One can write analogues of Guerra's replica symmetry breaking bound for such systems but it is not at all obvious how to choose informative functional order parameters in these bounds. We were able to make some progress for spherical pure p-sp...
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作者：Darses, Sebastien; Nourdin, Ivan
作者单位：Universite Marie et Louis Pasteur; Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given a-field Q. In our framework, we recall well-known results about Markov-Wiener diffusions. We then focus mainly on the case where X is a fractional diffusion and where 62 is the past, the future or the present of X. We treat some crucial examples and our main result is the existence of stochastic derivatives with respect to the present of X when X solves a stochastic diff...
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作者：Liggett, Thomas M.; Steif, Jeffrey E.; Toth, Balint
作者单位：University of California System; University of California Los Angeles; Chalmers University of Technology; University of Gothenburg
摘要：We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie-Weiss Ising model and includes as well all ferromagnetic Curie-Weiss Potts and Curie-Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide ...
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作者：Gaertner, Juergen; Koenig, Wolfgang; Molchanov, Stanislav
作者单位：Technical University of Berlin; University of North Carolina; University of North Carolina Charlotte; Leipzig University
摘要：We consider the parabolic Anderson problem partial derivative(t)u = Delta u + xi(x)u on R+ x Z(d) with localized initial condition u (0, x) = delta(0)(x) and random i.i.d. potential xi. Under the assumption that the distribution of xi(0) has a double-exponential, or slightly heavier, tail, we prove the following geometric characterization of intermittency: with probability one, as t -> infinity, the over-whelming contribution to the total mass Sigma x u(t, x) comes from a slowly increasing num...
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作者：Talet, Marina
作者单位：Aix-Marseille Universite
摘要：We study Brownian motion in a drifted Brownian potential. Kawazu and Tanaka [J. Math. Soc. Japan 49 (1997) 189-211] exhibited two speed regimes for this process, depending on the drift. They supplemented these laws of large numbers by central limit theorems, which were recently completed by Hu, Shi and Yor [Trans. Amen Math. Soc. 351 (1999) 3915-3934] using stochastic calculus. We studied large deviations [Ann. Probab. 29 (2001) 11731204], showing among other results that the rate function in ...
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作者：Goldstein, Larry
作者单位：University of Southern California
摘要：The zero bias distribution W* of W, defined though the characterizing equation EW f (W) = sigma(2) Ef ''(W*) for all smooth functions f, exists for all W with mean zero and finite variance sigma(2). For W and W* defined on the same probability space, the L-1 distance between F, the distribution function of W with EW = 0 and Var(W) = 1, and the cumulative standard normal phi has the simple upper bound parallel to F - Phi parallel to(1) <= vertical bar W-* - W vertical bar This inequality is use...
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作者：Holmes, Mark; Perkins, Edwin
作者单位：Euratom; University of British Columbia
摘要：We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the r-point functions and perhaps convergence of the survival probabilities. These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical ...
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作者：Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna
作者单位：University of Warsaw; University of Warsaw
摘要：We prove a functional limit theorem for the resealed occupation time fluctuations of a (d, alpha, beta)-branching particle system [particles moving in R-d according to a symmetric alpha-stable Levy process, branching law in the domain of attraction of a (1+ beta)-stable law, 0 < beta < 1, uniform Poisson initial state] in the case of intermediate dimensions, alpha / beta < d < alpha (1+ beta) / beta. The limit is a process of the form K gimel xi, where K is a constant, gimel is the Lebesgue me...
