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作者：Lawler, GF; Schramm, O; Werner, W
作者单位：Cornell University; Universite Paris Saclay; Microsoft
摘要：This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain D (subset of)(not equal) C is equal to the radial SLE2 path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that partial derivativeD is a C-1-simple closed curve, the same method is applied to show that the scaling limit of the uniform spanning tree Peano ...
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作者：Li, WV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let X = (X-t)(tis an element ofS) be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(sup(tis an element ofS)(X-t - X-t0) less than or equal to x) as x --> 0, with t(0) is an element of S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities...
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作者：Wang, FY
作者单位：Beijing Normal University
摘要：By using probabilistic approaches, some uniform gradient estimates are obtained for Dirichlet heat semigroups on a Riemannian manifold with boundary. As an application, lower bound estimates of isoperimetric constants are presented in terms of functional inequalities.
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作者：Fukushima, M; He, P; Ying, JG
作者单位：Kansai University; Shanghai University of Finance & Economics; Fudan University
摘要：We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.
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作者：Djellout, H; Guillin, A; Wu, L
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Wuhan University
摘要：We first give a characterization of the L-1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.
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作者：Li, XD
作者单位：University of Oxford; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We first prove the LP-convergence (p greater than or equal to 1) and a Fernique-type exponential integrability of divergence functionals for all Cameron-Martin vector fields with respect to the pinned Wiener measure on loop spaces over a compact Riemannian manifold. We then prove that the Driver flow is a smooth transform on path spaces in the sense of the Malliavin calculus and has an infinity-quasi-continuous modification which can be quasi-surely well defined on path spaces. This leads us t...
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作者：Hall, P; Wang, QY
作者单位：Australian National University; University of Sydney
摘要：The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation is used to give the exact rate of convergence in the central limit theorem up to order n(-1/2), wher...
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作者：Chen, LHY; Xia, AH
作者单位：National University of Singapore; University of Melbourne
摘要：The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem 2.3) in Poisson process approximation is proved by taking the local approach. It is obtained without reference to any particular metric, thereby allowing wider applicability. A Wasserstein pseudometric is introduced for measuring the accuracy of point process approximation. The ps...
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作者：Tarrés, P
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); University of Neuchatel
摘要：Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it has visited before. Pemantle and Volkov considered the case when the underlying graph is the one-dimensional integer lattice Z. They proved that the range is almost surely finite and that with positive probability the range contains exactly five points. They conjectured that this second event holds with probability 1....
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作者：Chang, CC; Landim, C; Lee, TY
作者单位：National Taiwan University; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a large deviations principle for the occupation time of a site in the two-dimensional symmetric simple exclusion process. The decay probability rate is of order t/logt and the rate function is given by Y-alpha(beta) = (pi/2){sin(-1)(2beta - 1) - sin(-1) (2alpha - 1))(2). The proof relies on a large deviations principle for the polar empirical measure which contains an interesting log scale spatial average. A contraction principle permits us to deduce the occupation time large deviatio...
