Relaxation in one-dimensional tropical sandpile

TL;DR

This paper studies the relaxation process in a one-dimensional tropical sandpile model, proving it terminates finitely and providing experimental evidence that the number of steps follows a power law.

Contribution

It establishes the finite termination of relaxation in the one-dimensional tropical sandpile and suggests a power law distribution for the number of steps involved.

Findings

Relaxation terminates after finitely many steps in 1D tropical sandpiles.

Experimental evidence indicates a power law for the number of relaxation steps.

The process deforms tropical hypersurfaces towards points.

Abstract

A relaxation in the tropical sandpile model is a process of deforming a tropical hypersurface towards a finite collection of points. We show that, in the one-dimensional case, a relaxation terminates after a finite number of steps. We present experimental evidence suggesting that the number of such steps obeys a power law.