A combinatorial identity for the speed of growth in an anisotropic KPZ model
Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 4, pp. 453-477.

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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/45
Classification : 05-XX, 60-XX, 82-XX
Mots-clés : Random surfaces, interacting particle systems, random tilings, limit shapes, determinantal processes, Kasteleyn matrices 
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Chhita, Sunil; Ferrari, Patrik L. A combinatorial identity for the speed of growth in an anisotropic KPZ model. Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 4, pp. 453-477. doi : 10.4171/aihpd/45. https://www.numdam.org/articles/10.4171/aihpd/45/
  • Nicoletti, Matthew; Petrov, Leonid Irreversible Markov dynamics and hydrodynamics for KPZ states in the stochastic six vertex model, Electronic Journal of Probability, Volume 28 (2023) no. none | DOI:10.1214/23-ejp1005
  • Lerouvillois, Vincent; Toninelli, Fabio Hydrodynamic limit for a 2D interlaced particle process, The Annals of Applied Probability, Volume 32 (2022) no. 1 | DOI:10.1214/21-aap1674
  • Nicoletti, Matthew; Petrov, Leonid Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model, arXiv (2022) | DOI:10.48550/arxiv.2201.12497 | arXiv:2201.12497
  • Assiotis, Theodoros Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays, Annales Henri Poincaré, Volume 21 (2020) no. 3, p. 909 | DOI:10.1007/s00023-019-00881-5
  • Chhita, Sunil; Ferrari, Patrik; Toninelli, Fabio Speed and fluctuations for some driven dimer models, Annales de l’Institut Henri Poincaré D, Volume 6 (2019) no. 4, pp. 489-532 | DOI:10.4171/aihpd/77
  • Chhita, Sunil; Toninelli, Fabio Lucio A (2 + 1)-Dimensional Anisotropic KPZ Growth Model with a Smooth Phase, Communications in Mathematical Physics, Volume 367 (2019) no. 2, p. 483 | DOI:10.1007/s00220-019-03402-x
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  • Laslier, Benoît; Toninelli, Fabio Lucio Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation, Communications in Mathematical Physics, Volume 358 (2018) no. 3, p. 1117 | DOI:10.1007/s00220-018-3095-y
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