Abstract
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.
Acknowledgments
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.
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. https://doi.org/10.1214/21-AOP1514
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