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math.PR2022
On some high-dimensional limits of matricial stochastic processes seen from a quantum probability perspective
Michaël Ulrich
We generalize the result of block-wise convergence of the Brownian motion on the unitary group towards a quantum Lévy process on the unitary dual group …
math.PR2015
Haar states and Lévy processes on the unitary dual group
Guillaume Cébron, Michaël Ulrich
We study states on the universal noncommutative *-algebra generated by the coefficients of a unitary matrix, or equivalently states on the unitary dual group. Its structure of dual…
math.PR2014★ 3 cited
Construction of a free Lévy process as high-dimensional limit of a Brownian motion on the Unitary group
Michaël Ulrich
It is well known that freeness appears in the high-dimensional limit of independence for matrices. Thus, for instance, the additive free Brownian motion can be seen as the limit of…