Open Access
2022 Chase-escape on the configuration model
Emma Bernstein, Clare Hamblen, Matthew Junge, Lily Reeves
Author Affiliations +
Electron. Commun. Probab. 27: 1-14 (2022). DOI: 10.1214/22-ECP470


Chase-escape is a competitive growth process in which red particles spread to adjacent empty sites according to a rate-λ Poisson process while being chased and consumed by blue particles according to a rate-1 Poisson process. Given a growing sequence of finite graphs, the critical rate λc is the largest value of λ for which red fails to reach a positive fraction of the vertices with high probability. We provide a conjecturally sharp lower bound and an implicit upper bound on λc for supercritical random graphs sampled from the configuration model with independent and identically distributed degrees with finite second moment. We additionally show that the expected number of sites occupied by red undergoes a phase transition and identify the location of this transition.

Funding Statement

All authors were partially supported by NSF Grants 2115936 and 2028892.


Download Citation

Emma Bernstein. Clare Hamblen. Matthew Junge. Lily Reeves. "Chase-escape on the configuration model." Electron. Commun. Probab. 27 1 - 14, 2022.


Received: 24 December 2021; Accepted: 9 May 2022; Published: 2022
First available in Project Euclid: 17 May 2022

MathSciNet: MR4424035
zbMATH: 1496.60116
Digital Object Identifier: 10.1214/22-ECP470

Primary: 60K35

Keywords: Interacting particle system , phase transition

Back to Top