Local Persistence in the Directed Percolation Universality Class

TL;DR

This paper improves estimates of local persistence exponents in directed percolation, explores corrections to scaling, introduces graded persistence, and investigates spatial persistence across different dimensions.

Contribution

It provides new estimates, introduces graded persistence, and extends the study of persistence to spatial dimensions in directed percolation.

Findings

Improved persistence exponent estimates in 1+1 dimensions.

Identification of strong corrections to scaling in higher dimensions.

Introduction of graded persistence probability and spatial persistence analysis.

Abstract

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we introduce a graded persistence probability that a site does not flip more than n times and demonstrate how local persistence can be studied in seed simulations. Finally, the problem of spatial (as opposed to temporal) persistence is investigated.