-
作者：Bárány, I
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London
摘要：For a convex body K in the plane, let p(n, K) denote the probability that n random, independent, and uniform points from K are in convex position, that is, none of them lies in the convex hull of the others. Here we determine the asymptotic behavior of p(n, K) by showing that, as n goes to infinity, n(2) (n)root(p(n, K)) tends to a finite and positive limit.
-
作者：Kallenberg, O
作者单位：Auburn University System; Auburn University
摘要：The ballot theorem and the uniform law for sojourn times, both results known for cyclically stationary sequences and processes on a bounded index set, are here extended to infinite, stationary sequences and to stationary processes on R+. Our extensions contain all previously known versions as special cases.
-
作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
-
作者：Pinelis, I
-
作者：Bobkov, SG
作者单位：Syktyvkar State University; University System of Georgia; Georgia Institute of Technology
摘要：We discuss an approach, based on the Brunn-Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In particular, we show that such measures have positive isoperimetric constants in the sense of Cheeger and thus always share Poincare-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.
-
作者：Daley, DJ
作者单位：Australian National University
摘要：A stationary renewal process N(.) for which the lifetime distribution has its hth moment finite or infinite according as k is less than or greater than kappa for some 1 < K < 2, is long-range dependent and has Hurst index alpha = (1/2)(3-kappa) (this is the critical index alpha for which lim sup(t-->infinity) t(-2a) var N(0, t] is finite or infinite according as a is greater than or less than alpha). This identification is accomplished by delineating the growth rate properties of the differenc...
-
作者：De Santis, E; Gandolfi, A
作者单位：Sapienza University Rome; University of Rome Tor Vergata
摘要：We study occurrence and properties of percolation of occupied bonds in systems with random interactions and, hence, frustration. We develop a general argument, somewhat like Peierls' argument, by which we show that in Z(d), d greater than or equal to 2, percolation occurs for all possible interactions (provided they are bounded away from zero) if the parameter p is an element of (0, 1), regulating the density of occupied bonds, is high enough. If the interactions are i.i.d. random variables th...
-
作者：Wang, QY; Jing, BY
作者单位：University of Wollongong; Hong Kong University of Science & Technology
摘要：In this paper we shall derive Exponential nonuniform Berry-Esseen bounds in the central limit theorem for self-normalized sums. We show that the size of the error can be reduced considerably by replacing the usual standardization by self-normalization. Tn particular, we establish the exponential bounds for the probability of the self-normalized sums under the condition that the third moment is finite, whereas an exponential moment assumption is required for the standardized sums. Applications ...
-
作者：Wu, L
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS)
-
作者：DeBlassie, RD
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Let X-t be reflected Brownian motion (RBM) in a cone with radially homogeneous reflection, killed upon reaching the vertex of the cone. We determine the adjoint process and use it to find the Martin boundary of the killed RBM together with all the corresponding positive harmonic functions. Then we can identify and prove uniqueness (up to positive scalar multiples) of the invariant measure for killed RBM and RBM without killing. Along the way, we prove the strong Feller property of the resolven...
