Exponential Convergence Rates of Second Quantization Semigroups and Applications

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 Lévy processes are investigated.

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