This event is a part of MJPS.
JSPS Open Partnership Joint Research Projects supported this seminar grant no.120249936 (PI Noriyoshi Sakuma).
Feb 11th @ K201
15:00 - 15:40 Kosuke Yamato (Osaka University)
Title: Entrance boundary for standard processes with no negative jumps and its application to exponential convergence to the Yaglom limit
Abstract: In this talk, I will discuss standard processes with no negative jumps under the entrance boundary condition. Similarly to one-dimensional diffusions, these processes can be turned into Feller processes by attaching the boundary point to the state space. The spectrum of the infinitesimal generator can be studied in detail using the scale function and is characterized by the zeros of an entire function. As an application, it is shown that under the strong Feller property, the convergence of the process killed at the boundary to the Yaglom limit is exponentially fast.
15:50 - 16:30 Arturo Jaramillo (CIMAT)
Title: Free Stein’s Method and the Berry-Esseen Theorem
Abstract: In this talk, I will introduce a formulation of Stein’s method for the semicircular distribution, tailored for the study of non-commutative variables. As a key application, I will discuss how this framework allows us to quantify the asymptotic semicircularity of sums of weakly dependent variables, using total variation distance as a measure. Moreover, I will highlight how moment matching of arbitrary order leads to improved convergence rates.
16:40 - 17:20 Kohki Iba (Osaka University)
Title: Conditioning to avoid bounded sets for a one dimensional Levy processes
Abstract: For several classes of bounded sets A, the limit of a one-dimensional Lévy process conditioned to avoid A up to a parametrized random time which tends to infinity. For A we take the set of finite points with several clocks and a bounded Fσ-set with exponential clock. We also take an integer lattice with exponential clock.
Feb 12th @ K201
15:00 - 15:40 Noriyoshi Sakuma (Osaka University)
Title: Generalized Meixner-type free gamma distributions: convolution formulas and potential correspondence
Abstract: We introduce and study a class of generalized Meixner-type free gamma distributions, which includes the free gamma distributions introduced by Anshelevich and certain scaled free beta prime distributions introduced by Yoshida. We investigate basic properties and mixture structures of these distributions. It greatly expands the range of free and classical correspondence via the potential function, which differs from the Bercovici-Pata bijection.
15:50 - 16:30 Josué Vazquez-Becerra (CIMAT)
Title: Annular noncrossing permutations in non-commutative probability.
Abstract: In this talk, we will first review some of the main properties of annular non-crossing permutations. Then, we will recall its initial connection to non-commutative probability, which relates to the description of second order freness of random matrices. Finally, we will present some connections to infinitesimal freeness and finite freeness.
16:40 - 17:20 Luca Lionni (École Normale Supérieure de Lyon)
Title: Free cumulants and freeness for unitarily invariant random tensors
Abstract: I will present some recent results concerning the construction of free cumulants for unitarily invariant random tensors, and the relations linking them to asymptotic moments. If time allows, I will explain the moments formulation of tensorial freeness and the generalization of non-commutative probability spaces. Based on work with Benoît Collins and Razvan Gurau.