概要：Poisson U-statistics are a fundamental class of Poisson functionals, with many examples arising in stochastic geometry. For such functionals, quantitative central limit theorems have been obtained using the Malliavin-Stein method for Poisson functionals. In this talk, I will present partial progress toward quantitative local central limit theorems for Poisson U-statistics and discuss applications to counting functionals arising from random geometric graphs.

概要：We first consider some involutions over a Markov chain, its quantum lift (quantum walk), and their scaling limits. Then will discuss zeta functions, trace formulas, and automorphic forms associated with the involutions, and their applications.