Quasi-stationary and quasi-ergodic distributions in the Pelikan random map

Samuel Brevitt; Rainer Klages

Quasi-stationary and quasi-ergodic distributions in the Pelikan random map

Chaotic Dynamics 2026-07-21 v1 Statistical Mechanics Mathematical Physics Dynamical Systems

Authors: Samuel Brevitt , Rainer Klages

Abstract

In this paper we present a concrete example of a substochastic discrete-time Markov chain on a countable state space producing a spectrum of infinitely many quasi-stationary distributions (QSDs) for generic parameter values, with each QSD supporting a distinct escape rate. Our system is motivated by an open variant of the Pelikan dynamical system, a random map introduced in the 1980s. These QSDs, and their stability to perturbative random noise, are tested in numerical simulations. The existence of unique QEDs is also established for some parameter values.

Keywords

quasi-stationary distributions quasi-ergodic distributions Pelikan random map substochastic Markov chain escape rate open dynamical systems

Cite

@article{arxiv.2607.19084,
  title  = {Quasi-stationary and quasi-ergodic distributions in the Pelikan random map},
  author = {Samuel Brevitt and Rainer Klages},
  journal= {arXiv preprint arXiv:2607.19084},
  year   = {2026}
}

Comments

18 pages, 9 figures