We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with distinct exponents. We study limiting behavior of interfaces which appear by such a strong competition. Consequently, three kinds of limiting behavior of interfaces (vanishing, moving and immovable interfaces as in ) are derived directly from our interacting particle system taking advantage of hydrodynamic limit procedure with singular limit for annihilation dynamics.
The author would like to thank Tadahisa Funaki, Hirokazu Ninomiya, Makiko Sasada and Kenkichi Tsunoda for giving him fruitful comments.
"Spatial-segregation limit for exclusion processes with two components under unbalanced reaction." Electron. J. Probab. 26 1 - 36, 2021. https://doi.org/10.1214/21-EJP621