Research PapersNo Access

MONOTONIC INDEPENDENCE ASSOCIATED WITH PARTIALLY ORDERED SETS

JANUSZ WYSOCZAŃSKI

Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

https://doi.org/10.1142/S0219025707002609Cited by:9 (Source: Crossref)

Abstract

A generalization of Muraki's notion of monotonic independence onto the case of partially ordered index set is given: algebras indexed by chains are monotonically independent, and algebras indexed by non-comparable elements are boolean independent. Examples of central limit theorem are shown in two cases. For the integral-points lattices ℕ^d the moments of the limit measure are related to the combinatorics of the finite heap-ordered labelled rooted trees (if d = 2). For the integral-points lattice ℕ × ℤ^d in Minkowski spacetime the limit measure is given by the recurrence of it's moments, which, for the case d = 1 is related to the inverse error function. Various formulas for computing mixed moments are shown to be related to the boolean-monotonic non-crossing pair partitions.

Research partially supported by KBN grant 2P03A00723, by the EU Research Training Network "QP-Applications", contract HPRN-CT-2002-00279 and by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge "Harmonic Analysis, Nonlinear Analysis and Probability" MTKD-CT-2004-013389.

Keywords:

AMSC: 46L54, 81R50

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