Permutation model for semi-circular systems and quantum random walks

Philippe Biane

Vol. 171 (1995), No. 2, 373–387

DOI: 10.2140/pjm.1995.171.373

Abstract

We give an approximation model for semi-circular families of non-commutative random variables, which is based on the permutation group. This model is compared to the random matrix model of Voiculescu, and a common refinement of the two approximations by explicit matrices with 0 – 1 entries is exhibited.

Mathematical Subject Classification 2000

Secondary: 81S25, 60J65

Milestones

Received: 29 July 1993

Published: 1 December 1995