Non stationarity of renewal processes with power-law tails

Claude Godrèche

Published 2019-09-25Version 1

Renewal processes generated by a power-law distribution of intervals with tail index less than unity are genuinely non stationary, even when the system, subjected to periodic boundary conditions, is translation invariant. This issue is illustrated by a critical review of the recent paper by Barma, Majumdar and Mukamel 2019 J. Phys. A 52 254001, devoted to the investigation of the properties of a specific one-dimensional equilibrium spin system with long-range interactions. We explain why discarding the non-stationarity of the process underlying the model leads to an incorrect expression of the critical spin-spin correlation function.