2017/08/13 by Alexander Gnedin, Gnedin, Alexander, Alexander Iksanov +5
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.1708.03938
openalex publication_date 2017/08/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Λ-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially n singletons we study the collision spectrum (Xn,k:2≤ k≤ n), where Xn,k counts, throughout the history of the process, the number of collisions involving exactly k blocks. Our focus is on the large n asymptotics of the joint distribution of the Xn,k's, as well as on functional limits for the bulk of the spectrum for simple coalescents. Similarly to the previous studies of the total number of collisions, the asymptotics of the collision spectrum largely depends on the behaviour of the measure Λ in the vicinity of 0. In particular, for beta(a,b)-coalescents different types of limit distributions occur depending on whether 02.