Spectral gap and convex concentration inequalities for birth–death processes
In this paper, we consider a birth–death process with generator and reversible invariant probability. Given an increasing function and the associated Lipschitz norm ‖⋅‖, we find an explicit formula for . As a typical application, with spectral theory, we revisit one variational formula of M. F. Chen for the spectral gap of in (). Moreover, by Lyons–Zheng’s forward-backward martingale decomposition theorem, we get convex concentration inequalities for additive functionals of...