Computing absorbing times via fluid approximations

Abstract

AbstractIn this paper we compute the absorbing timeTnof ann-dimensional discrete-time Markov chain comprisingncomponents, each with an absorbing state and evolving in mutual exclusion. We show that the random absorbing timeTnis well approximated by a deterministic timetnthat is the first time when a fluid approximation of the chain approaches the absorbing state at a distance 1 /n. We provide an asymptotic expansion oftnthat uses the spectral decomposition of the kernel of the chain as well as the asymptotic distribution ofTn, relying on extreme values theory. We show the applicability of this approach with three different problems: the coupon collector, the erasure channel lifetime, and the coupling times of random walks in high-dimensional spaces.