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

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.