A combinatorial identity for the speed of growth in an anisotropic KPZ model

TL;DR

This paper derives algebraic and combinatorial formulas for the growth speed in a generalized anisotropic KPZ model, extending previous results by analyzing the model's dynamics without relying on multi-time correlations.

Contribution

It provides new algebraic and combinatorial proofs for the growth speed in a generalized KPZ anisotropic model, where previous correlation-based methods were insufficient.

Findings

Derived algebraic expressions for growth speed

Provided combinatorial proofs for the same expressions

Extended understanding of KPZ anisotropic universality class

Abstract

The speed of growth for a particular stochastic growth model introduced by Borodin and Ferrari in [Comm. Math. Phys. 325 (2014), 603-684], which belongs to the KPZ anisotropic universality class, was computed using multi-time correlations. The model was recently generalized by Toninelli in [arXiv:1503.05339] and for this generalization the stationary measure is known but the time correlations are unknown. In this note, we obtain algebraic and combinatorial proofs for the expression of the speed of growth from the prescribed dynamics.