The Large-N Limits of Brownian Motions on GLN

Abstract

We introduce a two-parameter family of diffusion processes (B r,s(t))t≥0, r, s > 0, on the general linear group GLN that are Brownian motions with respect to certain natural metrics on the group. At the same time, we introduce a two-parameter family of free Itô processes (br,s(t))t≥0 in a faithful, tracial W ∗-probability space, and we prove that the full… (More)

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