On meteors, earthworms and WIMPs

TL;DR

This paper investigates a mass redistribution model on finite graphs, analyzing convergence to equilibrium and the distribution of empty sites and mass, linking these to random permutations with specific peak sets.

Contribution

It introduces new theorems connecting mass distribution and empty sites to the combinatorial structure of random permutations with peak sets.

Findings

Convergence to equilibrium is characterized for the model.

Distribution of mass at vertices is explicitly described.

Distribution of empty sites is linked to permutation peak sets.

Abstract

We study a model of mass redistribution on a finite graph. We address the questions of convergence to equilibrium and the rate of convergence. We present theorems on the distribution of empty sites and the distribution of mass at a fixed vertex. These distributions are related to random permutations with certain peak sets.