Sharp asymptotics for N-point correlation functions of coalescing heavy-tailed random walk

2025/05/08 by Jinjiong Yu, Yu, Jinjiong
Mathematics · Decision Sciences · #Stochastic processes and statistical mechanics #Probability and Risk Models #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2505.05000

Abstract

We study a system of coalescing continuous-time random walks starting from every site on ℤ, where the jump increments lie in the domain of attraction of an α-stable distribution with α∈(0,1]. We establish sharp asymptotics for the N-point correlation function of the system. Our analysis relies on two precise tail estimates for the system density, as well as the non-collision probability of N independent random walks with arbitrary fixed initial configurations. In addition, we derive refined estimates for heavy-tailed random walks, which may be of independent interest.

Citations

• Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications
• Notes on Random Walks in the Cauchy Domain of Attraction
• Coalescing systems of non-Brownian particles

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