Iterated logarithm law for sizes of clusters in Arratia flow

2013/10/24 by A. A. Dorogovtsev, Alexander Gnedin, Dorogovtsev, A. A. +3
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Primary 60J65 #Probability (math.PR) #Secondary 60D05 #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1310.6692

openalex publication_date 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotics of sizes of clusters for the Arratia flow is considered, the Arratia flow being a system of coalescing Wiener processes starting from the real axis and independent before they meet. A cluster at time t is defined as a set of particles that have glued together not later than at t. The results obtained are remarked to hold for any Arratia flow with a Lipschitz drift.

Related

• The central limit theorem for the number of clusters of the Arratia flow
• A Central Limit Theorem for Modified Massive Arratia Flow
• Gaussian structure in coalescing stochastic flows
• Representations of the finite-dimensional point densities in Arratia flows with drift
• Clustering rates and Chung type functional laws of the iterated logarithm for empirical and quantile processes