3 papers
math.OA2024
The Kummer distribution in free probability, and its characterizations
Marcin Świeca
We study the analogue of Kummer distribution in free probability. We prove characterization of free-Kummer and free Poisson distributions by freeness properties together with some…
math.OA2021
The Matsumoto-Yor property in free probability via subordination and Boolean cumulants
Marcin Świeca
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 assum…
math.PR2019
Multiplicity free actions, birth and death processes on partitions, and Biane's quantum Ornstein-Uhlenbeck semigroups
Wojciech Matysiak, Marcin Świeca
We introduce a family of multivariate continuous-time pure birth and pure death chains, with birth and death rates defined in terms of the generalized binomial coefficients for mul…