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The Matsumoto-Yor property in free probability via subordination and Boolean cumulants (2109.12545v1)
Published 26 Sep 2021 in math.OA
Abstract: We study the Matsumoto-Yor property in free probability. We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are subordination and Boolean cumulants. In particular, we establish a new connection between additive subordination function and Boolean cumulants.