Exponential convergence rates of second quantization semigroups and applications (Q2922427)

The authors consider the exponential convergence rate for the second quantization semigroups using the \(L_{2}\)-tail norm and convergence in entropy. Corresponding Dirichlet forms are defined and used to construct the parameters \(\lambda_{T}\) and \(\lambda_{E}\) associated with each form of convergence. The authors establish the required inequalities defining the convergence rate. An important and interesting example of application is provided, in fact, the authors derive the exponential convergence rates for birth-death-type Dirichlet forms on \(L_{2}(\pi_{\mu})\) with weighted function on \(\Gamma \times E\) and apply them to the path of a Lévy process.