We consider a family of multiplicative $(\lambda,\tau)$-Brownian motions on the general linear group parametrized by a real variance parameter $\lambda$ and a complex variance parameter $\tau$. We prove that, almost surely, their finite-dimensional marginals converge strongly, in the large-$N$ limit, to those of a family of free multiplicative $(\lambda,\tau)$-Brownian motions. This is a joint work with Mireille Capitaine and Guillaume CĂ©bron.
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