# Workshop on interactions between commutative and noncommutative probability

[[Program]]

09:30-09:40 Foreword

09:40-10:15 Thomas Simon (Université Lille 1)

Some properties of free stable densities

10:25-11:00 Kouji Yano (Kyoto University)

Some generalizations of refracted Levy processes

11:10-11:45 Takahiro Hasebe (Hokkaido University)

Free infinite divisibility for powers of random variables

11:45-13:15 Lunch

13:15-13:50 Hiroshi Tsukada (Osaka City University)

Remark on Tanaka formula for Lévy processes via Itô's stochastic calculus

13:55-14:30 Yuki Ueda (Hokkaido University)

Unimodality for classical and free Brownian motions with initial distributions

14:35-15:10 Muneya Matsui (Nanzan University)

Log-convexity and the cycle index polynomials with relation to compound Poisson distributions

15min break

15:25-16:00 Noriyoshi Sakuma (Aichi University of Education)

Selfdecomposable distributions in classical and free probability

16:05-16:40 Atsushi Takeuchi (Osaka City University)

Integration by parts formulas for Hawkes processes

16:45-17:20 Benoit Collins (Kyoto University)

Weingarten calculus through Weingarten orthogonality relations

(see the abstract below)

17:25-18:00 Christophe Profeta (Université d'Évry-Val-d'Essonne)

A stable Langevin model with diffusive-reflective boundary conditions

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[[Abstract]]

Benoit Collins (Kyoto University)

Title: Weingarten calculus through Weingarten orthogonality relations

Abstract: Weingarten calculus is about computing integrals of polynomial functions with respect to Hear measures on compact groups. The possibility of such a calculus was unveiled by theoretical physicists (including Weingarten) and put in a mathematical framework subsequently (by the presenter and many others). The initial mathematical formulations rely heavily on representation theoretic tools, however Weingarten heuristics relied on an overdetermined set of orthogonality relation. We revisit the very approach of Weingarten and formalize it. It allows us to interpret the Weingarten function as a harmonic function related to a random walk on an appropriate graph, and it yields the uniform estimates for the Weingarten function, which are the best known so far and optimal within a polynomial factor. This is joint work with Sho Matsumoto (Kagoshima).

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[[Organizers]]

Takahiro Hasebe (Hokkaido University)

Noriyoshi Sakuma (Aichi University of Education)

Kouji Yano (Kyoto University)