This talk is dedicated to the survey of some of our results related to q-deformations of the Fock spaces and related to q-convolutions for probability measures on the real line R. The main idea is done by the combinatorics of moments of the measures and related q-cumulants of different types. The main and interesting q-convolutions are related to classical continuous (discrete) q-Hermite polynomial. Among them are classical (q = 1) convolutions, the case q = 0, gives the free and Boolean relations, and the new class of q-analogue of classical convolutions done by Carnovole, Koornwinder, Biane, Anshelovich, and Kula. The related paper contains many questions and problems related to the positivity of that class of q-convolutions. The main result is the construction of Brownian motion related to q-Discrete Hermite polynomial of type I. Keywords — Ortogonal polynomials, Measures convolution, Khintchine inequality, q-Gaussian operators. For more details, see: Marek Bozejko, Wojciech Bozejko, (dedicated to Professor Jan Stochel on the occasion of his 70th birthday). Deformations and q-Convolutions. Old and New Results, Complex Analysis and Operator Theory (2024). https://link.springer.com/article/10.1007/s11785-024-01572-8
De Karol Penson
De Gérard Duchamp
De Jehanne Dousse
De Markus Reineke
De Maxim Kontsevich
De Arthemy Kiselev
De Toshiki Nakashima
De Joseph Ben Geloun
De Stéphane Dartois
De Yuki Kanakubo
De Yiannis Vlassopoulos
De Mohamed Ouerfelli
De Gérard Ben Arous
De Gérard Ben Arous
