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作者：Baudoin, Fabrice
作者单位：Purdue University System; Purdue University
摘要：We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions. The results are new even in the case of the Heisenberg group which is the simplest example of a sub-Riemanni...
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作者：Bally, Vlad; Caramellino, Lucia
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Inria; University of Rome Tor Vergata
摘要：We study the local existence and regularity of the density of the law of a functional on the Wiener space which satisfies a criterion that generalizes the Hormander condition of order one (i.e., involving the first-order Lie brackets) for diffusion processes.
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作者：Eisenbaum, Nathalie
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：A permanental vector with a symmetric kernel and index 2 is a squared Gaussian vector. The definition of permanental vectors is a natural extension of the definition of squared Gaussian vectors to nonsymmetric kernels and to positive indexes. The only known permanental vectors either have a positive definite kernel or are infinitely divisible. Are there some others? We present a partial answer to this question.
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作者：Nualart, David; Tudor, Ciprian A.
作者单位：University of Kansas; Universite de Lille; Bucharest University of Economic Studies
摘要：The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the determinant of its iterated Malliavin matrices. As an application, we show that the vector is not absolutely continuous if and only if its components are proportional.
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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...
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作者：Mourrat, Jean-Christophe; Weber, Hendrik
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Warwick
摘要：We show global well-posedness of the dynamic Phi(4) model in the plane. The model is a nonlinear stochastic PDE that can only be interpreted in a renormalised sense. Solutions take values in suitable weighted Besov spaces of negative regularity.
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作者：Jacob, Emmanuel; Morters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Bath
摘要：A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the d-dimensional torus and are connected to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering, we can independently tune the power law exponent tau of the degree distribu...
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作者：Rath, Balazs; Valesin, Daniel
作者单位：MTA-BME Stochastics Research Group; University of Groningen; Budapest University of Technology & Economics
摘要：The voter model on Z(d) is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When d >= 3, the set of (external) stationary distributions is a family of measures a, for a between 0 and 1. A configuration sampled from mu(alpha) is a strongly correlated field of 0's and l's on Zd in which the density of l's is a. We consider such a configuration as a site percolation model on Zd. We...
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作者：Dembo, Amir; Montanari, Andrea; Sen, Subhabrata
作者单位：Stanford University; Stanford University; Stanford University
摘要：For Erdos-Renyi random graphs with average degree gamma, and uniformly random gamma-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are n(gamma/4 + P-* root gamma/4 + o(root gamma)) + o(n) while the size of the minimum bisection is n(gamma/4 - P-* root gamma/4 + o(root gamma)) + o(n). Our derivation relates the free energy of the anti-ferromagnetic Ising model on such graphs to that of the SherringtonKirkpatrick model, with P-...
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作者：Krokowski, Kai; Reichenbachs, Anselm; Thaele, Christoph
作者单位：Ruhr University Bochum
摘要：A new Berry-Esseen bound for nonlinear functionals of nonsymmetric and nonhomogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete Ornstein-Uhlenbeck semigroup. The result is applied to subgraph counts and to the number of vertices having a prescribed degree in the Erd os-Renyi random graph. A further application deals with a percolation problem on trees.
