-
作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut; University of Cambridge
摘要：Let p(n)(y) = Sigma(k)(alpha) over cap (k)phi(y - k) + Sigma(jn-1)(l=0) Sigma(k)(beta) over cap (lk)2(l/2)psi(2(l) y-k) be the linear wavelet density estimator, where phi, psi are a father and a mother wavelet (with compact support), (alpha) over cap (k), (beta) over cap (lk) are the empirical wavelet coefficients based on an i.i.d. sample of random variables distributed according to a density p(0) on R, and j(n) is an element of Z, j(n) NE arrow infinity. Several uniform limit theorems are pr...
-
作者：Taylor, Jonathan E.; Adler, Robert J.
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz-Killing curvatures of these sets. Whereas our motivation is primarily probabilistic, with statistical applications in the background, this formula has also an interpretation as a version of the classic kinematic fundamental formula of integral geometry. All of these aspects ...
-
作者：Haas, Benedicte; Pitman, Jim; Winkel, Matthias
作者单位：Universite PSL; Universite Paris-Dauphine; University of California System; University of California Berkeley; University of Oxford
摘要：We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second applica...
-
作者：Bourgade, P.
作者单位：Sorbonne Universite
摘要：We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension it. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension p. The developed method leads to the following result: for this conditional measure, writing Z(U)((p)) for the first nonzero derivative of the characteristic polynomial at 1, Z(U)((p))/p! =(law) Pi(n-p)(l=1)(1-X(l)), the X(l)'s being explicit independent random...
-
作者：Bertoin, Jean
作者单位：Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider a (sub-)critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton-Watson processes and a version of the ballot theorem. Some limit theorem...
-
作者：Balogh, Jozsef; Bollobas, Bela; Morris, Robert
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Cambridge; University of Memphis; University of Cambridge
摘要：By bootstrap percolation we mean the following deterministic process on a graph G. Given a set A of vertices infected at time 0, new vertices are subsequently infected, at each time step, if they have at least r is an element of N previously infected neighbors. When the set A is chosen at randorn, the main aim is to determine the critical probability p(c)(G, r) at which percolation (infection of the entire graph) becomes likely to occur. This bootstrap process has been extensively studied on t...
-
作者：Mountford, Thomas; Schonmann, Roberto H.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of California System; University of California Los Angeles
摘要：We study the threshold theta contact process on Z(d) with infection parameter lambda. We show that the critical point lambda(c), defined as the threshold for survival starting from every site occupied, vanishes as d -> infinity. This implies that the threshold theta voter model on Z(d) has a nondegenerate extremal invariant measure, when d is large.
-
作者：Howitt, Chris; Warren, Jon
作者单位：University of Warwick
摘要：Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice Z. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random proportion distributed according to some specified probability measure on [0, 1] and dividing the mass in that proportion. One part then moves to each of the two adjacent sites. This paper considers a continuous analogue of this evolution, which may be described by means of a st...
-
作者：Wang, Dong
作者单位：Brandeis University
摘要：We solve the largest sample eigenvalue distribution problem in the rank I spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge. We observe a phase change phenomenon similar to that in the complex case, and prove that the new distribution at the phase change point is the GOE Tracy-Widom distribution.
-
作者：Barbu, Viorel; Da Prat, Giuseppe; Tubaro, Luciano
作者单位：Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Trento
摘要：We consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Sigma in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Sigma.
