S. Chhita, P.L. Ferrari and F.L. Toninelli Speed and fluctuations for some driven dimer models preprint: arXiv:1705.07641 2017 https://arxiv.org/abs/1705.07641
Abstract: We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ universality class. We use a combinatorial approach to determine the speed of growth and show logarithmic growth in time of the variance of the height function fluctuations.
2016
V. Beffara, S. Chhita and K. Johansson Airy point process at the liquid-gas boundary arXiv:1606.08653 2016 http://arxiv.org/abs/1606.08653
Abstract: {Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.}
S. Chhita, P.L. Ferrari and H. Spohn Limit distributions for KPZ growth models with spatially homogeneous random initial conditions preprint, arXiv:1611.06690 2016 http://arxiv.org/abs/1611.06690
Abstract: For stationary KPZ growth in 1+1 dimensions the height fluctuations are governed by the Baik-Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the roughness of the initial conditions. The distributions are defined through a variational formula. We use Monte Carlo simulations to obtain their numerical plots. Also discussed is the connection to the six-vertex model at is conical point.
2015
Sunil Chhita and Patrik L. Ferrari A combinatorial identity for the speed of growth in an anisotropic KPZ model arXiv e-prints 2015 http://arxiv.org/abs/1508.01665
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.
2014
Sunil Chhita and Kurt Johansson Domino statistics of the two-periodic Aztec diamond arXiv e-prints 2014 http://arxiv.org/abs/1410.2385
Abstract: Random domino tilings of the Aztec diamond shape exhibit interesting features and some of the statistical properties seen in random matrix theory. As a statistical mechanical model it can be thought of as a dimer model or as a certain random surface. We consider the Aztec diamond with a two-periodic weighting which exhibits all three possible phases that occur in these types of models, often referred to as solid, liquid and gas. To analyze this model, we use entries of the inverse Kasteleyn matrix which give the probability of any configuration of dominoes. A formula for these entries, for this particular model, was derived by Chhita and Young (2014). In this paper, we find a major simplication of this formula expressing entries of the inverse Kasteleyn matrix by double contour integrals which makes it possible to investigate their asymptotics. In a part of the Aztec diamond we use this formula to show that the entries of the inverse Kasteleyn matrix converge to the known entries of the full-plane inverse Kasteleyn matrices for the different phases. We also study the detailed asymptotics of the covariance between dominoes at both the 'solid-liquid' and 'liquid-gas' boundaries. Finally we provide a potential candidate for a combinatorial description of the liquid-gas boundary.