The \(N\)-limit of spectral gap of a class of birth-death Markov chains (Q2722278)

This paper is devoted to the study of the limit behaviour of spectral gaps of a class of Markov chains and it pursues the following two objectives: 1) representation of a new exposition of the theory of Zeifman's method for bounding the spectral gap of birth-death Markov chains; it is demonstrated that the method is applicable to general Markov chains; 2) implementation of a method to study the asymptotic behaviour of the spectral gap of a class of birth-death processes known as random walks on complete graphs.NEWLINENEWLINENEWLINEA particular case of the result proves the conjecture by \textit{P. Diaconis} and \textit{L. Saloff-Coste} [Probab. Theory Relat. Fields 105, No. 3, 393-421 (1996; Zbl 0847.60081)] on the spectral gap of an ergodic time-homogeneous and reversible Markov chain on the finite state space.