Welcome seminar. Positivity and Gaussian processes.

We will present relations between positive definite kernels (also operator valued) and classical and quantum Gaussian processes following the paper of Yanqui Qiu - "On a result of Bozejko on extension of positive definite kernels" - arXiv - 2019 and Bull. London Math.Soc 2019 and the results of E.Hirai, T.Hirai and A.Hora and M.Guta and myself on Thoma representations of central positive definite functions on Coxeter groups of type A and B, i.e. on permutations group and sign-permutation group on infinite many letters.