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作者：Delarue, Francois; Diel, Roland
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a -Holder continuous function, . Regularity of the ...
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作者：Nicolaescu, Liviu I.
作者单位：University of Notre Dame
摘要：We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet theorem stating that if the bundle and the manifold are oriented, then the Euler form of the above connection can be identified, as a current, with the expectation of the random current defined by the zero-locus of a random section in the above Gaussian ensemble.
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作者：Doney, R. A.; Rivero, V.
作者单位：University of Manchester
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作者：Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Institute of Science & Technology - Austria
摘要：We consider random matrices of the form H = W + lambda V, lambda is an element of R+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i. i. d. entries that are independent of W. We assume subexponential decay of the distribution of the matrix entries of W and we choose lambda similar to 1, so that the eigenvalues of W and lambda V are typically of the same order. Further, we assume that the density of the en...
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作者：Li, Xue-Mei
作者单位：University of Warwick
摘要：Consider a family of random ordinary differential equations on a manifold driven by vector fields of the form where are vector fields, is a positive number, is a diffusion process taking values in possibly a different manifold, are annihilators of . Under Hormander type conditions on we prove that, as approaches zero, the stochastic processes converge weakly and in the Wasserstein topologies. We describe this limit and give an upper bound for the rate of the convergence.
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作者：Gu, Yu; Mourrat, Jean-Christophe
作者单位：Stanford University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.
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作者：Curien, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：Pursuing the approach of Angel and Ray (Ann Probab, 2015) we introduce and study a family of random infinite triangulations of the full-plane that satisfy a natural spatial Markov property. These new random lattices naturally generalize Angel and Schramm's uniform infinite planar triangulation (UIPT) and are hyperbolic in flavor. We prove that they exhibit a sharp exponential volume growth, are non-Liouville, and that the simple random walk on them has positive speed almost surely. We conjectu...
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作者：Eberle, Andreas
作者单位：University of Bonn
摘要：We consider contractivity for diffusion semigroups w.r.t. Kantorovich ( Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown that by appropriate explicit choices of the underlying distance, contractivity with rates of close to optimal order can be obtained in several fundamental classes of examples where contractivity w.r.t. standard Wasserstein distances fails. Applications include ov...
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作者：Goetze, F.; Tikhomirov, A.
作者单位：University of Bielefeld; Syktyvkar State University; Russian Academy of Sciences; Komi Science Centre of the Ural Branch of the Russian Academy of Sciences
摘要：Let X = (X-jk)(j,k=1)(n) denote a Hermitian random matrix with entries X-jk, which are independent for 1 <= j <= k <= n. We consider the rate of convergence of the empirical spectral distribution function of the matrix X to the semi-circular law assuming that EX (jk) = 0, EXjk2 = 1 and that sup(n >= 1) sup(1 <= j, k <= n) E vertical bar X-jk vertical bar(4) =: mu(4) < infinity, and sup(1 <= j,k <= n) vertical bar X-jk vertical bar <= D(0)n(1/4) By means of a recursion argument it is shown that...
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作者：Barlow, Martin; Burdzy, Krzysztof; Timar, Adam
作者单位：University of British Columbia; University of Washington; University of Washington Seattle; Szeged University
摘要：We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold.
