SU(d)-biinvariant random walks on SL(d,C) and their Euclidean counterparts
نویسنده
چکیده
Motivated by recent results of A. Klyachko, we construct a probability preserving, isometric isomorphism from the Banach algebra Mb(SL(d,C)‖SU(d)) of all SU(d)-biinvariant bounded signed measures on SL(d,C) to some Banach subalgebra of the Banach algebra of all bounded signed measures on the Euclidean space of all Hermitian d × d-matrices with trace 0. This isomorphism leads to strong limit theorems for the singular spectrum of SU(d)-biinvariant random walks on SL(d,C). Our construction of the isomorphism relies on deformations of hypergroup convolutions related to these groups and will be carried out generally for complex connected semisimple Lie groups with finite center and maximal compact subgroups.
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