Abstract
This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type A or a. Under suitable scaling, the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.
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Acknowledgements
The author thanks his Ph.D. supervisor Shanjian Tang, researcher Kai Du and vice professor Jing Zhang for their advice in the past 5 years. Meanwhile, he also cherishes the anonymous reviewers’ valuable and helpful comments which improve the quality of this article.
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Zhao, T. Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction. Chin. Ann. Math. Ser. B 43, 195–208 (2022). https://doi.org/10.1007/s11401-022-0311-z
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DOI: https://doi.org/10.1007/s11401-022-0311-z