-
作者：Kortchemski, Igor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We study large random dissections of polygons. We consider random dissections of a regular polygon with n sides, which are chosen according to Boltzmann weights in the domain of attraction of a stable law of index theta is an element of (1, 2]. As n goes to infinity, we prove that these random dissections converge in distribution toward a random compact set, called the random stable lamination. If theta = 2, we recover Aldous' Brownian triangulation. However, if theta is an element of (1, 2), ...
-
作者：Rhodes, Remi; Sohier, Julien; Vargas, Vincent
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Eindhoven University of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous e...
-
作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：In this paper, we study the long-term asymptotics for the quenched moment E-x exp{integral(t)(0) V (B-s) ds} consisting of a d-dimensional Brownian motion {B-s; s >= 0} and a generalized Gaussian field V. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433-453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional whit...
-
作者：Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Chinese University of Hong Kong; Hong Kong University of Science & Technology
摘要：Let x(1),...,x(n) be a random sample from a p-dimensional population distribution, where p = p(n) -> infinity and log p = o(n(beta)) for some 0 < beta <= 1, and let L-n be the coherence of the sample correlation matrix. In this paper it is proved that root n/log pL(n) -> 2 in probability if and only if Ee(t0 vertical bar x11 vertical bar alpha) < infinity for some t(0) > 0, where alpha satisfies beta = alpha/(4 - alpha). Asymptotic distributions of L-n are also proved under the same sufficient...
-
作者：Last, Guenter; Moerters, Peter; Thorisson, Hermann
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; University of Iceland
摘要：Let B = (B-t)(t epsilon R) be a two-sided standard Brownian motion. An unbiased shift of B is a random time T, which is a measurable function of B, such that (BT+t - B-T)(t epsilon R) is a Brownian motion independent of B-T. We characterise unbiased shifts in terms of allocation rules balancing mixtures of local times of B. For any probability distribution nu on R we construct a stopping time T >= 0 with the above properties such that B-T has distribution nu. We also study moment and minimalit...
-
作者：Ding, Jian
作者单位：Stanford University; University of Chicago
摘要：In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, assuming that the maximal hitting time is significantly smaller than the cover time. Previously, this was only proved for regular trees and the 2D lattice. Furthermore, for general trees, we derive exponential concentration for the cover time,...
-
作者：Eisenbaum, Nathalie
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We solve a conjecture raised by Evans in 1991 on the characterization of the positively correlated squared Gaussian vectors. We extend this characterization from squared Gaussian vectors to permanental vectors. As side results, we obtain several equivalent formulations of the property of infinite divisibility for squared Gaussian processes.
-
作者：Nourdin, Ivan; Rosinski, Jan
作者单位：Universite de Lorraine; University of Tennessee System; University of Tennessee Knoxville
摘要：We characterize the asymptotic independence between blocks consisting of multiple Wiener-Ito integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension and other related results on the multivariate convergence of multiple Wiener-Ito integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long-range dependent st...
-
作者：Berkes, Istvan; Liu, Weidong; Wu, Wei Biao
作者单位：Graz University of Technology; Shanghai Jiao Tong University; University of Chicago
摘要：The celebrated results of Komlos, Major and Tusnady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functi...
-
作者：Gess, Benjamin
作者单位：Humboldt University of Berlin
摘要：Unique existence of solutions to porous media equations driven by continuous linear multiplicative space time rough signals is proven for initial data in L-1(O) on bounded domains O. The generation of a continuous, order-preserving random dynamical system on L-1(O) and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. The random attractor is shown to be compact and attracting in L-infinity(O) norm. ...
