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On Q-independence, limit theorems and q-Gaussian distribution

Marcin Marciniak (1998)

Studia Mathematica

We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.

On quenched and annealed critical curves of random pinning model with finite range correlations

Julien Poisat (2013)

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

This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q -order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron–Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for q = 1 and q = 2 and a weak disorder asymptotic in the general case....

On random fractals with infinite branching: definition, measurability, dimensions

Artemi Berlinkov (2013)

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

We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

On random split of the segment

Milena Bieniek, Dominik Szynal (2005)

Applicationes Mathematicae

We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These...

On randomized stopping times.

Concepción Arenas Solá (1990)

Trabajos de Estadística

In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.

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