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作者：Berger, Noam; Deuschel, Jean-Dominique
作者单位：Hebrew University of Jerusalem; Technical University of Berlin
摘要：We consider a random walk on , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from to nearest neighbor is the same as to nearest neighbor . Assuming that the environment is genuinely -dimensional and balanced we show a quenched invariance principle: for almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend bo...
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作者：Hedenmalm, Haakan; Nieminen, Pekka J.
作者单位：Royal Institute of Technology; University of Helsinki
摘要：We relate the Gaussian free field on a planar domain to the variational formula of Hadamard which explains the change of the Green function under a perturbation of the domain. This is accomplished by means of a natural integral operator-called the Hadamard operator-associated with a given flow of growing domains.
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作者：Borodin, Alexei; Corwin, Ivan
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters . We prove several results about these processes, which include the following. (1) We explicitly evaluate expectations of a rich family of observables for these processes. (2) In the case , we find a Fredholm determinant formula for a -Laplace transform of the distribution of the last part of the Macdonald-rand...
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作者：Mourrat, Jean-Christophe
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimensi...
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作者：Friz, Peter; Oberhauser, Harald
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its L,vy area) as rough path noise the solution coincides with the standard variational solution of the SPDE.
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作者：Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie; Tetali, Prasad
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Paris Nanterre; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Pr,kopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings. To illustrate through examples, we apply our results to the complete graph and to the hypercube for which our results are optimal-...
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作者：Kabluchko, Zakhar; Klimovsky, Anton
作者单位：Ulm University; Leiden University; Leiden University - Excl LUMC
摘要：The partition function of the random energy model at inverse temperature is a sum of random exponentials , where are independent real standard normal random variables (=random energies), and . We study the large N limit of the partition function viewed as an analytic function of the complex variable . We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the ra...
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作者：Gamarnik, David
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The paper is devoted to the problem of establishing right-convergence of sparse random graphs. This concerns the convergence of the logarithm of number of homomorphisms from graphs or hyper-graphs to some target graph . The theory of dense graph convergence, including random dense graphs, is now well understood (Borgs et al. in Ann Math 176:151-219, 2012; Borgs et al. in Adv Math 219:1801-1851, 2008; Chatterjee and Varadhan in Eur J Comb 32:1000-1017, 2011; Lovasz and Szegedy in J Comb Theory ...
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作者：Espinasse, T.; Gamboa, F.; Loubes, J-M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper, using spectral theory of Hilbertian operators, we study a special class of Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their asymptotic optimality.
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作者：Grimmett, Geoffrey R.; Manolescu, Ioan
作者单位：University of Cambridge
摘要：In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the se...
