Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation

TL;DR

This paper studies how particles in a one-dimensional self-gravitating system aggregate over time, revealing a phase transition where the growth rate of the largest cluster shifts from logarithmic to polynomial depending on initial particle speeds.

Contribution

It introduces a detailed analysis of aggregation dynamics in one-dimensional gravitational systems, highlighting a phase transition based on initial velocities.

Findings

Logarithmic growth of largest cluster in cold gas

Polynomial growth in warm gas

Identification of a phase transition in aggregation behavior

Abstract

We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic behavior of L_n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (``cold'' gas) L_n has logarithmic order of growth while higher speeds (``warm'' gas) yield polynomial rates for L_n.