A generalised Biane process. (English) Zbl 0701.60104

Parthasarathy, K. R.

Séminaire de probabilités XXIV 1988/89, Lect. Notes Math. 1426, 345-348 (1990).

[For the entire collection see Zbl 0695.00024.]
Using the methods of quantum probability in a toy Fock space and the Peter-Weyl theory of representations of a compact group G, a class of random walks is constructed on the state space of all irreducible characters of G. Such a construction was outlined by Ph. Biane [see the preceding review, Zbl 0701.60103] for the group \(SU_ 2\).

Reviewer: K.R.Parthasarathy

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G50	Sums of independent random variables; random walks
46L51	Noncommutative measure and integration
46L53	Noncommutative probability and statistics
46L54	Free probability and free operator algebras
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

quantum probability; Fock space

Citations:

Zbl 0695.00024; Zbl 0701.60103