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A noncommutative version of a Theorem of Marczewski for submeasures

Paolo de Lucia, Pedro Morales (1992)

Studia Mathematica

It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.

A projective central limit theorem and interacting Fock space representation for the limit process

Vitonofrio Crismale (2007)

Banach Center Publications

Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.

A remark on p-convolution

Rafał Sałapata (2011)

Banach Center Publications

We introduce a p-product of algebraic probability spaces, which is the definition of independence that is natural for the model of noncommutative Brownian motions, described in [10] (for q = 1). Using methods of the conditionally free probability (cf. [4, 5]), we define a related p-convolution of probability measures on ℝ and study its relations with the notion of subordination (cf. [1, 8, 9, 13]).

Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

An De Rijdt, Nikolas Vander Vennet (2010)

Annales de l’institut Fourier

The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C * -algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary...

Asymptotic spectral analysis of generalized Erdős-Rényi random graphs

Song Liang, Nobuaki Obata, Shuji Takahashi (2007)

Banach Center Publications

Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.

Asymptotic spectral analysis of growing graphs: odd graphs and spidernets

Daisuke Igarashi, Nobuaki Obata (2006)

Banach Center Publications

Two new examples are given for illustrating the method of quantum decomposition in the asymptotic spectral analysis for a growing family of graphs. The odd graphs form a growing family of distance-regular graphs and the two-sided Rayleigh distribution appears in the limit of vacuum spectral distribution of the adjacency matrix. For a spidernet as well as for a growing family of spidernets the vacuum distribution of the adjacency matrix is the free Meixner law. These distributions are calculated...

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