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Article Dans Une Revue Infinite Dimensional Analysis, Quantum Probability and Related Topics Année : 2021

Schur–Weyl duality and the product of randomly-rotated symmetries by a unitary Brownian motion

Nizar Demni
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Tarek Hamdi
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Résumé

In this paper, we introduce and study a unitary matrix-valued process which is closely related to the Hermitian matrix-Jacobi process. It is precisely defined as the product of a deterministic self-adjoint symmetry and a randomly-rotated one by a unitary Brownian motion. Using stochastic calculus and the action of the symmetric group on tensor powers, we derive an ordinary differential equation for the moments of its fixed-time marginals. Next, we derive an expression of these moments which involves a unitary bridge between our unitary process and another independent unitary Brownian motion. This bridge motivates and allows to write a second direct proof of the obtained moment expression.

Dates et versions

hal-03338344 , version 1 (08-09-2021)

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Citer

Nizar Demni, Tarek Hamdi. Schur–Weyl duality and the product of randomly-rotated symmetries by a unitary Brownian motion. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2021, 24 (01), pp.2150002. ⟨10.1142/S0219025721500028⟩. ⟨hal-03338344⟩
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