Projection Method for Moment Bounds on Order Statistics from Restricted Families: II. Independent Case

The method of projection, proposed in Part I, is applied to derive sharp moment bounds for the expectations of order statistics based onindependentsamples from restricted families of distributions. Three families are considered: life distributions with decreasing failure density, decreasing failure rate, and symmetric unimodal ones. The respective bounds are also numerically compared with those for general populations in both the dependent and independent cases.     

Weak laws of large numbers for cooperative gamblers

Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables. The class of applicable distributions, herein described, extends beyond that for sample means, but even for sample means our theory offers new results concerning the characterization of explicit norming sequences. The general form of the latter characterization for linear combinations also yields a surprising new result in the theory of slow variation. Work was supported in part by the Hungarian Scientific Research Fund, Grant T048360, and carried out within the Analysis and Stochastics Research Group of the Hungarian Academy of Sciences.     

Conditional limiting distribution of beta-independent random vectors

The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W² is a beta distributed random variable with parameters m/2,(d−m)/2 and (U₁,…,U_m),(U_m+1,…,U_d) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.     

Expectation of intrinsic volumes of random polytopes

Let K be a convex body in ℝ ^d , let j ∈ {1, …, d−1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C ₊², then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C ₊³) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to the case when the only condition on K is that a ball rolls freely inside K. Funded by the Marie-Curie Research Training Network “Phenomena in High-Dimensions” (MRTN-CT-2004-511953).     

Discrete universality of the <Emphasis Type="Italic">L</Emphasis>-functions of elliptic curves

A discrete universality theorem is obtained in the Voronin sense for the L-functions of elliptic curves. We use the difference of an arithmetical progression h > 0 such that \(\exp \left\{ {\frac{{2\pi k}}{h}} \right\}\) is rational for some k ≠ 0. A limit theorem in the space of analytic functions plays a crucial role in the proof.     

Infinite volume limit of the Abelian sandpile model in dimensions d ≥ 3

We study the Abelian sandpile model on . In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning forest measure on .      

Invariant or quasi-invariant probability measures for infinite dimensional groups

Deterministic Euler flow on a torus cannot leave invariant any probability measure.

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Exploiting the performance of dictionary-based bio-entity name recognition in biomedical literature

Bio-entity name recognition is the key step for information extraction from biomedical literature. This paper presents a dictionary-based bio-entity name recognition approach. The approach expands the bio-entity name dictionary via the Abbreviation Definitions identifying algorithm, improves the recall rate through the improved edit distance algorithm and adopts some post-processing methods including Pre-keyword and Post-keyword expansion, Part of Speech expansion, merge of adjacent bio-entity names and the exploitation of the contextual cues to further improve the performance. Experiment results show that with this approach even an internal dictionary-based system could achieve a fairly good performance.     

Small deviations of series of independent positive random variables with weights close to exponential

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