Laws of large numbers in the raise and peel 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 TQ equation applied to the associated XXZ chain and on its solution at obtained by Fridkin, Stroganov and Zagier.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 July 2019
 DOI:
 10.1088/17425468/ab2ccd
 arXiv:
 arXiv:1903.10093
 Bibcode:
 2019JSMTE..07.4003P
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 20 pages, 4 figures