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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 269 - Seminar in Combinatorics
Dr. Akihiro Miyagwa
UC San Diego
Q-deformation of independent Gaussian random variables in non-commutative probability
Abstract:
In 1970, Frisch and Bourret introduced a q-deformation of independent Gaussian random variables (say "q-Gaussian system"). In one-variable case, q-Gaussian is the distribution whose orthogonal polynomials are q-Hermite polynomials, and this distribution interpolates between Rademacher (q=-1), semicircle (q=0), Gaussian (q=1) distribution. In multivariable case, q-Gaussian system is represented as a tuple of operators (which are non-commutative in general) on the q-deformed Fock space introduced by Bożejko and Speicher.
In this talk, I will explain related combinatorics (pair partitions and number of crossings) and analysis for q-Gaussian system.
January 7, 2025
2:00 PM
APM 7321
Research Areas
Combinatorics****************************
