Comment on "Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-Dimensional Random Environments"

TL;DR

This paper provides a rigorous derivation of persistence properties in Sinai's model, showing they are valid for a broad class of asymmetric hopping models beyond the original assumptions.

Contribution

It offers a transparent, rigorous derivation of persistence predictions and extends their validity to general asymmetric hopping models.

Findings

Predictions can be derived from simple random walk properties.

Results are valid for any asymmetric hopping model, not just the random force model.

Applicability extends beyond the critical point.

Abstract

In a recent letter [PRL 80 (1998) 3539] Fisher, Le Doussal and Monthus report new predictions for the persistence properties of Sinai's model, which they obtain by using an approximate real space renormalization group scheme. In this comment we show that these predictions can be derived in a rigorous and more transparent way by reducing the quantities of interest to particular statistical properties of a simple random walk in a homogeneous environment. We also point out that they are valid in a much more general context: our results are neither restricted to the random force model but are valid for any asymmetric hopping model, nor to the vicinity of the critical point.