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作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：Recently, Auffinger, Ben Arous and Cerny initiated the study of critical points of the Hamiltonian in the spherical pure p-spin spin glass model, and established connections between those and several notions from the physics literature. Denoting the number of critical values less than Nu by Crt(N) (u), they computed the asymptotics of 1/N log(ECrt(N) (u)), as N, the dimension of the sphere, goes to infinity. We compute the asymptotics of the corresponding second moment and show that, for p >= ...
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作者：Toninelli, Fabio Lucio
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We introduce a class of (2 + 1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. Irreversible means that the interface has an average nonzero drift. Interface configurations correspond to height functions of dimer coverings of the infinite hexagonal or square lattice. The model can also be viewed as an interacting driven particle system and in the totally asymmetric case the dynamics corresponds to an infinite collection of mutua...
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作者：Brzeniak, Zdzislaw; Motyl, Elzbieta; Ondrejat, Martin
作者单位：University of York - UK; University of Lodz; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：Building upon a recent work by two of the authors and J. Seidler on bw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an invariant measure to stochastic 2-D Navier-Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.
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作者：Damron, Michael; Lam, Wai-Kit; Wang, Xuan
作者单位：University System of Georgia; Georgia Institute of Technology; Indiana University System; Indiana University Bloomington
摘要：We consider first passage percolation on Z(2) with i.i.d. weights, whose distribution function satisfies F(0) = p(c) = 1/2. This is sometimes known as the critical case because large clusters of zero-weight edges force passage times to grow at most logarithmically, giving zero time constant. Denote T (0, partial derivative B(n)) as the passage time from the origin to the boundary of the box [-n, n] x [-n, n]. We characterize the limit behavior of T (0, partial derivative B (n)) by conditions o...
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作者：Wang, Feng-Yu
作者单位：Tianjin University; Swansea University
摘要：By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the nonexplosion of solutions as well as the existence, uniqueness and regularity estimates of invariant probability measures. These conditions include a class of drifts unbounded on compact domains such that the usual Lyapunov conditions cannot be verified. The main results are extended to second-order differential op...
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作者：Hsu, Elton P.; Wang, Yu; Wang, Zhenan
作者单位：Northwestern University; University of Washington; University of Washington Seattle
摘要：Under general conditions, we devise a stochastic version of De Giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form partial derivative(t)u = div(A del u) + f(t, x, u) + g(i)(t, x, u)<(w)over dot>(i)(t) with progressively measurable diffusion coefficients. We use the scheme to show that the solution of the equation is almost surely Holder continuous in both space and time variables.
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Goldschmidt, Christina; Miermont, Gregory
作者单位：McGill University; University of Oxford; University of Oxford; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Consider the minimum spanning tree (MST) of the complete graph with n vertices, when edges are assigned independent random weights. Endow this tree with the graph distance renormalized by n(1/3) and with the uniform measure on its vertices. We show that the resulting space converges in distribution as n -> infinity to a random compact measured metric space in the Gromov-Hausdorff-Prokhorov topology. We additionally show that the limit is a random binary R-tree and has Minkowski dimension 3 alm...
