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作者：Deya, Aurelien; Panloup, Fabien; Tindel, Samy
作者单位：Universite de Lorraine; Universite d'Angers; Purdue University System; Purdue University
摘要：We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter H is an element of (1/3, 1) and multiplicative noise component sigma. When sigma is constant and for every H is an element of (0, 1), it was proved in [Ann. Probab. 33 (2005) 703-758] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order t(-alpha) where alpha is an eleme...
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作者：Hairer, Martin; Xu, Weijun
作者单位：Imperial College London; University of Oxford; New York University; NYU Shanghai
摘要：We extend the weak universality of KPZ in [An analytic BPHZ theorem for regularity structures (2016)] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.
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作者：Basak, Anirban; Rudelson, Mark
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Weizmann Institute of Science; University of Michigan System; University of Michigan
摘要：For a class of sparse random matrices of the form A(n) = (xi(i, j)delta(i, j))(i)(n), j=1 where {xi(i, j)} are i.i.d. centered sub-Gaussian random variables of unit variance, and {delta(i, j)} are i.i.d. Bernoulli random variables taking value 1 with probability p(n), we prove that the empirical spectral distribution of An/root np(n) converges weakly to the circular law, in probability, for all p(n) such that p(n) = omega (log(2) n/n). Additionally if p(n) satisfies the inequality np(n) > exp(...
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作者：Alexander, Yotam; Eldan, Ronen
作者单位：Weizmann Institute of Science
摘要：We show that the convex hull of the path of Brownian motion in n-dimensions, up to time 1, is a smooth set. As a consequence we conclude that a Brownian motion in any dimension almost surely has no cone points for any cone whose dual cone is nontrivial.
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作者：Bae, Joohak; Kang, Jaehoon; Kim, Panki; Lee, Jaehun
作者单位：Seoul National University (SNU); University of Bielefeld; Seoul National University (SNU)
摘要：In this paper, we study the transition densities of pure-jump symmetric Markov processes in R-d, whose jumping kernels are comparable to radially symmetric functions with mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of the transition densities (heat kernel estimates) for such processes. This is the first study on global heat kernel estimates of jump processes (including non-Levy processes) whose weak scaling index is not...
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作者：De March, Hadrien; Touzi, Nizar
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Martingale transport plans on the line are known from Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R-d, d >= 1. Our decomposition is a partition of R-d consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well defined. We justify the re...
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作者：Bao, Zhigang; Erdos, Laszlo; Schnelli, Kevin
作者单位：Hong Kong University of Science & Technology; Institute of Science & Technology - Austria; Royal Institute of Technology
摘要：Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Sigma be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189-1217] asserts that the empirical eigenvalue distribution of the matrix X : = U Sigma V* converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in C. Within the bulk regime, that is, in the interior o...
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作者：Deya, Aurelien
作者单位：Universite de Lorraine
摘要：We study a d-dimensional wave equation model (2 <= d <= 4) with quadratic nonlinearity and stochastic forcing given by a space-time fractional noise. Two different regimes are exhibited, depending on the Hurst parameter H = (H-0, ... , H-d) is an element of (0, 1)(d+1) of the noise: If Sigma(d)(i=0) H-i > d - 1/2, then the equation can be treated directly, while in the case d - 3/4 < Sigma(d)(i=0) H-i <= d - 1/2, the model must be interpreted in the Wick sense, through a renormalization proced...
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作者：Austin, Tim
作者单位：University of California System; University of California Los Angeles
摘要：Let K-1, ..., K-n, be bounded, complete, separable metric spaces. Let lambda(i) be a Borel probability measure on K-i for each i. Let f : Pi(i) K-i -> R be a bounded and continuous potential function, and let mu(dx) proportional to e(f(x))lambda(1)(dx(1)) ... lambda(n) (dx(n)) be the associated Gibbs distribution. At each point x is an element of Pi(i) K-i, one can define a 'discrete gradient' del f (x, .) by comparing the values of f at all points which differ from x in at most one coordinate...
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作者：Cipriani, Alessandra; Dan, Biltu; Hazra, Rajat Subhra
作者单位：Delft University of Technology; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：On the integer lattice, we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in d >= 2. Namely, it is shown that the scaling limit in d = 2, 3 is a Holder continuous random field, while in d >= 4 the membrane model converges to a random distribution. As a by-product of the proof in d = 2, 3, we obtain the scaling limit of the max...
