FREE BROWNIAN MOTION AND EVOLUTION TOWARDS ⊞-INFINITE DIVISIBILITY FOR k-TUPLES

DOI10.1142/S0129167X09005303zbMath1173.46306arXiv0711.3787OpenAlexW2963617571MaRDI QIDQ3636307

Alexandru Nica, Serban Teodor Belinschi

Publication date: 30 June 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3787

zbMATH Keywords

free Brownian motioninfinite divisibilityfree additive convolution

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54)

Related Items (12)

Relations between convolutions and transforms in operator-valued free probability ⋮ Generators of some non-commutative stochastic processes ⋮ Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants ⋮ On the supports of measures in free multiplicative convolution semigroups ⋮ Some geometric properties of the subordination function associated to an operator-valued free convolution semigroup ⋮ Non-crossing linked partitions, the partial order ≪ on 𝑁𝐶(𝑛), and the 𝑆-transform ⋮ Relations between infinitesimal non-commutative cumulants ⋮ Appell polynomials and their relatives. III: Conditionally free theory ⋮ Multi-variable subordination distributions for free additive convolution ⋮ Convolution powers in the operator-valued framework ⋮ An operad of non-commutative independences defined by trees ⋮ On operator-valued infinitesimal Boolean and monotone independence

Cites Work

• Addition of freely independent random variables
• Stable laws and domains of attraction in free probability theory
• Multiplicative functions on the lattice of non-crossing partitions and free convolution
• \(\eta\)-series and a Boolean Bercovici--Pata bijection for bounded \(k\)-tuples
• Lectures on the Combinatorics of Free Probability

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