Sticky dispersion on the complete graph: a kinetic approach

TL;DR

This paper investigates a kinetic approach to a dispersion process on the complete graph, providing analytical insights and numerical results within a mean-field framework, and introduces a novel econophysics reinterpretation.

Contribution

It offers a new kinetic perspective on the dispersion process, contrasting with previous probabilistic methods, and introduces a novel econophysics model for analysis.

Findings

Analytical results on large time behavior of the mean-field dynamics

Supporting numerical illustrations of the dispersion process

Reinterpretation of the model in terms of econophysics

Abstract

We study a variant of the dispersion process on the complete graph introduced in the recent work [17] under the mean-field framework. We adopt a kinetic perspective (as opposed to the probabilistic approach taken in [17] and many other related works) thanks to the reinterpretation of the model in terms of a novel econophysics model. Various analytical and quantitative results regarding the large time behaviour of the mean-field dynamics are obtained and supporting numerical illustrations are provided.