## A generalised Biane process.(English)Zbl 0701.60104

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
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