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作者：Osekowski, Adam
作者单位：University of Warsaw
摘要：We present a probabilistic study of the Hilbert operator, T f (x) = 1/pi integral(infinity)(0) f(y) dy/x+y, x >= 0, defined on integrable functions f on the positive halfline. Using appropriate novel estimates for orthogonal martingales satisfying the differential subordination, we establish sharp moment, weak-type and phi-inequalities for T. We also show similar estimates for higher dimensional analogues of the Hilbert operator, and by the further careful modification of martingale methods, w...
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作者：Garet, Olivier; Gouere, Jean-Baptiste; Marchand, Regine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Tours; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：We study the number N-n of open paths of length n in supercritical oriented percolation on Z(d) x N, with d >= 1, and we prove the existence of the connective constant for the supercritical oriented percolation cluster: on the percolation event {inf N-n > 0}, N-n(1/n) almost surely converges to a positive deterministic constant. The proof relies on the introduction of adapted sequences of regenerating times, on subadditive arguments and on the properties of the coupled zone in supercritical or...
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作者：Li, Liping; Ying, Jiangang
作者单位：Fudan University
摘要：The main purpose of this paper is to explore the structure of regular Dirichlet subspaces of one-dimensional Brownian motion. As stated in [Osaka J. Math. 42 (2005) 27-41], every such regular Dirichlet subspace can be characterized by a measure-dense set G. When G is open, F = G(c) is the boundary of G and, before leaving G, the diffusion associated with the regular Dirichlet subspace is nothing but Brownian motion. Their traces on F still inherit the inclusion relation, in other words, the tr...
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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...
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作者：Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Given some essentially separable filtration (Zn)(n <= 0) indexed by the non-positive integers, we define the notion of complementability for the filtrations contained in (Zn)(n <= 0). We also define and characterize the notion ofmaximality for the poly-adic sub-filtrations of (Zn)(n <= 0). We show that any poly-adic sub-filtration of (Zn)(n <= 0) which can be complemented by a Kolmogorovian filtration is maximal in (Zn)(n <= 0). We show that the converse is false, and we prove a partial conver...
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作者：Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
作者单位：University of Washington; University of Washington Seattle; University of North Carolina; University of North Carolina Chapel Hill
摘要：We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I. This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional l...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore; Brown University
摘要：Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection (SDER) and the so-called submartingale problem. We consider a general formulation of the submartingale problem for (obliquely) reflected diffusions in domains with piecewise C2 boundaries and piecewise continuous reflection vector fields. Under suitable assumptions, we show that well-posedness of the submartingale problem is equivalent to existence and uniqueness in...
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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...
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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...
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作者：Banuelos, Rodrigo; Davis, Burgess
