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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 .

60K35Interacting random processes; statistical mechanics type models; percolation theory
60G50Sums of independent random variables; random walks
46L51Noncommutative measure and integration
46L53Noncommutative probability and statistics
46L54Free probability and free operator algebras
60J10Markov chains (discrete-time Markov processes on discrete state spaces)