Annales de l’Institut Henri Poincaré D


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Volume 4, Issue 4, 2017, pp. 453–477
DOI: 10.4171/AIHPD/45

Published online: 2017-12-04

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

Sunil Chhita[1] and Patrik L. Ferrari[2]

(1) Bonn University, Germany
(2) Bonn University, Germany

The speed of growth for a particular stochastic growth model introduced by Borodin and Ferrari in [5], which belongs to the KPZ anisotropic universality class, was computed using multi-time correlations. The model was recently generalized by Toninelli in [38] and for this generalization the stationarymeasure 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.

Keywords: Random surfaces, interacting particle systems, random tilings, limit shapes, determinantal processes, Kasteleyn matrices

Chhita Sunil, Ferrari Patrik: A combinatorial identity for the speed of growth in an anisotropic KPZ model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 (2017), 453-477. doi: 10.4171/AIHPD/45