Exponential Convergence Rates of Second Quantization Semigroups and Applications

TL;DR

This paper characterizes exponential convergence rates of second quantization semigroups in $L^2$-tail norm and entropy, extending known results and applying them to birth-death processes on Poisson spaces and Lévy process path spaces.

Contribution

It provides a new characterization of convergence rates for second quantization semigroups using the base Dirichlet form, expanding the theoretical understanding.

Findings

Established exponential convergence rates in $L^2$-tail norm and entropy.

Applied results to birth-death processes on Poisson spaces.

Analyzed convergence on Lévy process path spaces.

Abstract

Exponential convergence rates in the $L^2$-tail norm and entropy are characterized for the second quantization semigroups by using the corresponding base Dirichlet form. This supplements the well known result on the $L^2$-exponential convergence rate of second quantization semigroups. As applications, birth-death type processes on Poisson spaces and the path space of L\'evy processes are investigated.