Active Phase for the Stochastic Sandpile on Z

TL;DR

This paper proves that the critical threshold for the one-dimensional stochastic sandpile model is below one, confirming a conjecture and advancing understanding of phase transitions in such systems.

Contribution

It establishes that the critical value for the model is less than one, verifying a key conjecture in the field.

Findings

Critical value is less than one.

Confirms conjecture of Rolla and Sidoravicius.

Advances understanding of phase transition in stochastic sandpiles.

Abstract

We prove that the critical value of the one-dimensional Stochastic Sandpile Model is less than one. This verifies a conjecture of Rolla and Sidoravicius.