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Tail and moment estimates for sums of independent random vectors with logarithmically concave tails

Rafał Latała (1996)

Studia Mathematica

Let X i be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable X = ∑ v i X i , where v i are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.

Teoría ergódica y simetrización.

Francesc Bofill (1982)

Stochastica

We study the relations between simetrization by a limiting process of probabilities and functions defined on a metric compacy product space and their ergodic properties.

The distribution of eigenvalues of randomized permutation matrices

Joseph Najnudel, Ashkan Nikeghbali (2013)

Annales de l’institut Fourier

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter θ > 0 ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....

The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces

Nguyen Van Huan, Nguyen Van Quang (2012)

Kybernetika

We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.

The Dyson Brownian Minor Process

Mark Adler, Eric Nordenstam, Pierre Van Moerbeke (2014)

Annales de l’institut Fourier

Consider an n × n Hermitean matrix valued stochastic process { H t } t ≥ 0 where the elements evolve according to Ornstein-Uhlenbeck processes. It is well known that the eigenvalues perform a so called Dyson Brownian motion, that is they behave as Ornstein-Uhlenbeck processes conditioned never to intersect.In this paper we study not only the eigenvalues of the full matrix, but also the eigenvalues of all the principal minors. That is, the eigenvalues of the k × k minors in the upper left corner of H t . Projecting this...

The fuzzy metric space based on fuzzy measure

Jialiang Xie, Qingguo Li, Shuili Chen, Huan Huang (2016)

Open Mathematics

In this paper, we study the relation between a fuzzy measure and a fuzzy metric which is induced by the fuzzy measure. We also discuss some basic properties of the constructed fuzzy metric space. In particular, we show that the nonatom of fuzzy measure space can be characterized in the constructed fuzzy metric space.

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

Ashkan Nikeghbali, Dirk Zeindler (2013)

Annales de l'I.H.P. Probabilités et statistiques

The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...

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