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September 2021 Chase-escape with death on trees
Erin Beckman, Keisha Cook, Nicole Eikmeier, Sarai Hernandez-Torres, Matthew Junge
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Ann. Probab. 49(5): 2530-2547 (September 2021). DOI: 10.1214/21-AOP1514


Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the variant in which red particles die and describe the phase diagram for the resulting process on infinite d-ary trees. A novel connection to weighted Catalan numbers makes it possible to characterize the critical behavior.

Funding Statement

Hernandez-Torres was supported by fellowship from the Mexican National Council for Science and Technology (CONACYT). Eikmeier was partially supported by NSF RAPID DMS Grant #2028892. Junge was partially supported by NSF DMS Grant #1641020 as well as NSF RAPID DMS Grant #2028892.


Thanks to David Sivakoff and Joshua Cruz for helpful advice and feedback. We are also grateful to Sam Francis Hopkins for pointing us to a reference about weighted Catalan numbers. Feedback during the review process greatly improved the final version. The research was initiated during the 2019 AMS Mathematical Research Community in Stochastic Spatial Systems.


Download Citation

Erin Beckman. Keisha Cook. Nicole Eikmeier. Sarai Hernandez-Torres. Matthew Junge. "Chase-escape with death on trees." Ann. Probab. 49 (5) 2530 - 2547, September 2021.


Received: 1 May 2020; Revised: 1 February 2021; Published: September 2021
First available in Project Euclid: 24 September 2021

Digital Object Identifier: 10.1214/21-AOP1514

Primary: 60C05 , 60K35
Secondary: 05A15

Keywords: Growth process , phase transition

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 5 • September 2021
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