# Laws of large numbers in the Raise and Peel model

## TL;DR

This paper proves exact laws of large numbers for key quantities in the Raise and Peel model, linking stochastic processes with integrable systems, and confirming related conjectures about stationary state correlations.

## Contribution

It introduces a novel application of Baxter's T-Q equation to establish laws of large numbers in the Raise and Peel model, connecting stochastic dynamics with integrable quantum chains.

## Key findings

- Exact laws of large numbers for tile removal and avalanches
- Validation of conjectured stationary state correlations
- Application of Baxter's T-Q equation to stochastic model

## Abstract

We establish the exact laws of large numbers for two time additive quantities in the Raise and Peel model, the number of tiles removed by avalanches and the number of global avalanches happened by given time. The validity of conjectures for the related stationary state correlation functions then follow. The proof is based on the technique of Baxter's T-Q equation applied to the associated XXZ chain and on its solution at $\Delta=-1/2$ obtained by Fridkin, Stroganov and Zagier.