-
作者：Campese, Simon
作者单位：University of Rome Tor Vergata
摘要：We prove a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. [Ann. Prob. 38 (2010) 396-438] and Rosen [Stoch. Dyn. 11 (2011) 5-48], which were later reproven by Hu and Nualart [Electron. Commun. Probab. 15 (2010) 396-410] and Rosen [In Seminaire de Probabilites XLIII (2011) 95-104 Springer] are included. Furthermore, a conjecture of Rosen for the fourth moment is settled: In comparison...
-
作者：Rahman, Mustazee; Virag, Balint
作者单位：University of Toronto
摘要：We show that the largest density of factor of i.i.d. independent sets in the d-regular tree is asymptotically at most (log d)/d as d -> infinity. This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random d-regular graphs have the same asymptotic density. In contrast, the density of the largest independent sets in these graphs is asymptotically 2(log d)/d. We prove analogous results for Poisson-Galton-Watson tr...
-
作者：Baccelli, Francois; Haji-Mirsadeghij, Mir-Omid
作者单位：University of Texas System; University of Texas Austin; Sharif University of Technology
摘要：A compatible point-shift F maps, in a translation invariant way, each point of a stationary point process (1) to some point of Phi. It is fully determined by its associated point-map, f, which gives the image of the origin by F. It was proved by J. Mecke that if F is bijective, then the Palm probability of Phi is left invariant by the translation of -f. The initial question motivating this Paper is the following generalization of this invariance result: in the non-bijective case, what probabil...
-
作者：Kane, Daniel
作者单位：University of California System; University of California San Diego; University of California System; University of California San Diego
摘要：We prove a structural result for degree-d polynomials. In particular, we show that any degree-d polynomial, p can be approximated by another polynomial, pp, which can be decomposed as some function of polynomials q1,...,qm with qi normalized and m = O-d(1), so that if X is a Gaussian random variable, the probability distribution on (qi (X),..,qm(X)) does not have too much mass in any small box. Using this result, we prove improved versions of a number of results about polynomial threshold func...
-
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.
-
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...
-
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...
