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作者：Friz, Peter K.; Zorin-Kranich, Pavel
作者单位：Technical University of Berlin; University of Bonn
摘要：We establish a new scale of p-variation estimates for martingale para-products, martingale transforms and Ito integrals, of relevance in rough paths theory, stochastic and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartin-gales and (controlled) rough paths and their integration theory.
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作者：Hofmanova, Martina; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We are concerned with the three-dimensional incompressible Navier- Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in L2 we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result, in partic-ular, implies nonuniqueness in law. Second, we prove nonuniqueness of the associated Markov processes in a suitably...
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作者：Kozma, Gady; Samotij, Wojciech
作者单位：Weizmann Institute of Science; Tel Aviv University
摘要：We show that the naive mean-field approximation correctly predicts the leading term of the logarithmic lower tail probabilities for the number of copies of a given subgraph in G(n, p) and of arithmetic progressions of a given length in random subsets of the integers in the entire range of densities where the mean-field approximation is viable.Our main technical result provides sufficient conditions on the maximum degrees of a uniform hypergraph ?-L that guarantee that the logarithmic lower tai...
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作者：Thoma, Eric
作者单位：New York University
摘要：We characterize the behavior of a random discrete interface phi on [-L, L](d) boolean AND Z(d) with energy Sigma V (Delta phi(x)) as L -> infinity, where Delta is the discrete Laplacian and V is a uniformly convex, symmetric, and smooth potential. The interface phi is called the non-Gaussian membrane model. By analyzing the Helffer-Sjostrand representation, associated to Delta phi, we provide a unified approach to continuous scaling limits of the rescaled and interpolated inter-face in dimensi...
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作者：Chen, Xin; LI, Xue-mei; Wu, Bo
作者单位：Shanghai Jiao Tong University; Imperial College London; Fudan University
摘要：The main results of the article are short time estimates and asymptotic estimates for the first two order derivatives of the logarithmic heat kernel of a complete Riemannian manifold. We remove all curvature restrictions and also develop several techniques.A basic tool developed here is intrinsic stochastic variations with pre-scribed second order covariant differentials, allowing to obtain a path inte-gration representation for the second order derivatives of the heat semigroup Pt on a comple...
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作者：Hutchroft, Tom; Michta, Emmanue; Slade, Gordon
作者单位：California Institute of Technology; University of British Columbia
摘要：We consider percolation on Z(d) and on the d-dimensional discrete torus, in dimensions d >= 11 for the nearest-neighbour model and in dimensions d > 6 for spread-out models. For Z(d) we employ a wide range of techniques and previous results to prove that there exist positive constants c and C such that the slightly subcritical two-point function and one-arm probabilities satisfy Ppc-epsilon(0 <-> x) <= C/||x||(d-2) e(-c epsilon 1/2) ||x|| c/r(2)e -C epsilon(1/2r) <= Ppc-epsilon (0 <-> partial ...
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作者：Dey, Partha s.; Terlov, G. R. I. G. O. R. Y.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In the seventies, Charles Stein revolutionized the way of proving the cen-tral limit theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to adapt and strengthen this method to a variety of different set-tings and other limiting distributions. However, it has not been yet extended to study conditional convergences. In this article we develop a novel approach, using Stein's method for exchangeable ...
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作者：Cuny, C.; Dedecker, J.; Merlevede, F.; Peligrad, M.
作者单位：Universite de Bretagne Occidentale; Universite Paris Cite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：Let A(n) = epsilon(n) center dot center dot center dot epsilon(1), where (epsilon n)n >= 1 is a sequence of independent random matrices, taking values in GL(d)(R), d >= 2, with common distribution mu. In this paper, under standard assumptions on mu (strong irreducibility and prox-imality) we prove Berry-Esseen type theorems for log(||A(n)||) when mu has a polynomial moment. More precisely, we get the rate ((logn)/n)(q/2-1), when mu has a moment of order q is an element of[2, 3] and the rate 1/...
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作者：Nutz, Marcel; Wiesel, Johannes
作者单位：Columbia University; Columbia University
摘要：We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr delta dinger potentials, describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian or, ...
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作者：Diaconu, Simona
作者单位：Stanford University
摘要：The Tracy-Widom distributions are among the most famous laws in probability theory, partly due to their connection with Wigner matrices. In particular, for A = 1/root n(a(ij))(1 <= i,j <= n) is an element of R-nxn symmetric with (a(ij))(1 <= i <= j <= n) i.i.d. standard normal, the fluctuations of its largest eigenvalue lambda(1)(A) are asymptotically described by a real-valued Tracy-Widom distribution TW1 : n(2/3)(lambda(1)(A) - 2) double right arrow TW1. As it often happens, Gaussianity can ...
