-
作者：PITTEL, B
摘要：In a set of even cardinality n, each member ranks all the others in order of preference. A stable matching is a partition of the set into n/2 pairs, with the property that no two unpaired members both prefer each other to their partners under matching. It is known that for some problem instances no stable matching exists. What if an instance of the ranking system is chosen uniformly at random? We show that the mean and the variance of the total number of stable matchings for the random problem...
-
作者：RIO, E
摘要：Let (X(i))i is-an-element-of Z+d be an array of independent identically distributed zero-mean random vectors with values in R(k). When E(\X1\r) < + infinity, for some r > 2, we obtain the strong approximation of the partial sum process (SIGMA(i is-an-element-of nuS)X(i): S is-an-element-of l) by a Gaussian partial sum process (SIGMA(i is-an-element-of nuS)Y(i): S is-an-element l), uniformly over all sets in a certain Vapnik-Cher-vonenkis class l of subsets of [0, 1]d. The most striking result ...
-
作者：ALDOUS, D
摘要：Let (R(k), k greater-than-or-equal-to 1) be random trees with k leaves, satisfying a consistency condition: Removing a random leaf from R(k) gives R(k - 1). Then under an extra condition, this family determines a random continuum tree l, which it is convenient to represent as a random subset of l1. This leads to an abstract notion of convergence in distribution, as n --> infinity, of (rescaled) random trees T(n) on n vertices to a limit continuum random tree l. The notion is based upon the ass...
-
作者：CHEN, X
摘要：In this paper we establish some general forms of the law of the iterated logarithm for independent random variables (X(n)) with Banach space values, where (X(n)) is not necessarily identically distributed. Our results include the Kolmogorov law of the iterated logarithm (LIL) in both finite and infinite dimensional cases, and they improve the Wittmann LIL as well as extend it to the vector setting. The Ledoux-Talagrand LIL for an i.i.d. sequence is also a simple corollary of our results.
-
作者：NGUYEN, BG; YANG, WS
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：In this paper, we apply the Brydges-Spencer lace expansion and the Hara-Slade analysis to obtain the triangle condition for the nearest-neighbor oriented bond percolation in high dimensions and for the spread-out oriented bond percolation in Z(d) X Z, d greater than or equal to 5. Furthermore, we also establish the infrared bound in the subcritical region and the mean-field behavior for these models.
-
作者：ROSINSKI, J; SAMORODNITSKY, G
作者单位：Cornell University
摘要：Subadditive functionals on the space of sample paths include suprema, integrals of paths, oscillation on sets and many others. In this paper we find an optimal condition which ensures that the distribution of a subadditive functional of sample paths of an infinitely divisible process belongs to the subexponential class of distributions. Further, we give exact tail behavior for the distributions of such functionals, thus improving many recent results obtained for particular forms of subadditive...
-
作者：SZNITMAN, AS
作者单位：New York University
摘要：We consider Brownian motion evolving among killing traps. We develop a technique of ''enlargement of obstacles.'' This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according t...
-
作者：DILWORTH, SJ; MONTGOMERYSMITH, SJ
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Let X = Sigma epsilon(n)x(n) be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable parallel to X parallel to in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.
-
作者：CHANG, FC; KEMPERMAN, JHB; STUDDEN, WJ
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Let LAMBDA be the set of probability measures lambda on [0, 1]. Let M(n) = {(c1,..., c(n))\lambda is-an-element-of LAMBDA), where c(k) = c(k)(lambda) = integral-1/0x(k) dlambda, k = 1, 2,... are the ordinary moments, and assign to the moment space M(n) the uniform probability measure P(n). We show that, as n --> infinity, the fixed section (c1,..., c(k)), properly normalized, is asymptotically normally distributed. That is, square-root n[(c1,..., c(k)) - (c1(0),..., c(k)0] converges to MVN(0, ...
-
作者：MYKLAND, PA
摘要：The paper contains a ''smoothed'' one-step triangular array asymptotic expansion for discrete-time martingales. An important element of the proof is a second-order description of Skorokhod embedding of discrete martingales in continuous ones. An application to Markov processes is given, along with a bootstrapping example.
