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

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