A stochastic min-driven coalescence process and its hydrodynamical limit

TL;DR

This paper studies a stochastic particle system where particles merge with the smallest particle, proving its convergence to a deterministic limit and analyzing the minimal size evolution.

Contribution

It introduces a new stochastic coalescence process constrained by minimal size and establishes its hydrodynamical limit.

Findings

Convergence of the stochastic process to a deterministic PDE.

Characterization of the minimal size evolution over time.

Insights into the behavior of constrained coagulation systems.

Abstract

A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalised version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.