All Outputs (15)

GOE fluctuations for the maximum of the top path in alternating sign matrices (2023)
Journal Article
Ayyer, A., Chhita, S., & Johansson, K. (2023). GOE fluctuations for the maximum of the top path in alternating sign matrices. Duke Mathematical Journal, 172(10), 1961-2104. https://doi.org/10.1215/00127094-2022-0075

The six-vertex model is an important toy-model in statistical mechanics for two-dimensional ice with a natural parameter ∆. When ∆ = 0, the so-called free-fermion point, the model is in natural correspondence with domino tilings of the Aztec diamond.... Read More about GOE fluctuations for the maximum of the top path in alternating sign matrices.

On the domino shuffle and matrix refactorizations (2023)
Journal Article
Chhita, S., & Duits, M. (2023). On the domino shuffle and matrix refactorizations. Communications in Mathematical Physics, 401(2), 1417-1467. https://doi.org/10.1007/s00220-023-04676-y

This paper is motivated by computing correlations for domino tilings of the Aztec diamond. It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is, the two-periodic... Read More about On the domino shuffle and matrix refactorizations.

Local geometry of the rough-smooth interface in the two-periodic Aztec diamond (2021)
Journal Article
Beffara, V., Chhita, S., & Johansson, K. (2022). Local geometry of the rough-smooth interface in the two-periodic Aztec diamond. Annals of Applied Probability, 32(2), 974-1017. https://doi.org/10.1214/21-aap1701

Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay... Read More about Local geometry of the rough-smooth interface in the two-periodic Aztec diamond.

Correlations in totally symmetric self-complementary plane partitions (2021)
Journal Article
Ayyer, A., & Chhita, S. (2021). Correlations in totally symmetric self-complementary plane partitions. Transactions of the London Mathematical Society, 8(1), 493-526. https://doi.org/10.1112/tlm3.12039

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon... Read More about Correlations in totally symmetric self-complementary plane partitions.

The domino shuffling algorithm and Anisotropic KPZ stochastic growth (2020)
Journal Article
Chhita, S., & Toninelli, F. L. (2021). The domino shuffling algorithm and Anisotropic KPZ stochastic growth. Annales Henri Lebesgue, 4, 1005-1034. https://doi.org/10.5802/ahl.95

The domino-shuffling algorithm [EKLP92a, EKLP92b, Pro03] can be seen as a stochastic process describing the irreversible growth of a (2+1)-dimensional discrete interface [CT19, Zha18]. Its stationary speed of growth 𝑣𝚠(𝜌) depends on the average inter... Read More about The domino shuffling algorithm and Anisotropic KPZ stochastic growth.

Speed and fluctuations for some driven dimer models (2019)
Journal Article
Chhita, S., Ferrari, P., & Toninelli, F. (2019). Speed and fluctuations for some driven dimer models. Annales de l’Institut Henri Poincaré D, 6(4), 489-532. https://doi.org/10.4171/aihpd/77

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 cla... Read More about Speed and fluctuations for some driven dimer models.

A (2 + 1)-dimensional anisotropic KPZ growth model with a smooth phase (2019)
Journal Article
Chhita, S., & Toninelli, F. L. (2019). A (2 + 1)-dimensional anisotropic KPZ growth model with a smooth phase. Communications in Mathematical Physics, 367(2), 483-516. https://doi.org/10.1007/s00220-019-03402-x

Stochastic growth processes in dimension (2+1) were conjectured by D. Wolf, on the basis of renormalization-group arguments, to fall into two distinct universality classes, according to whether the Hessian Hρ of the speed of growth v(ρ) as a function... Read More about A (2 + 1)-dimensional anisotropic KPZ growth model with a smooth phase.

Airy Point Process at the liquid-gas boundary (2018)
Journal Article
Beffara, V., Chhita, S., & Johansson, K. (2018). Airy Point Process at the liquid-gas boundary. Annals of Probability, 46(5), 2973-3013. https://doi.org/10.1214/17-aop1244

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. Th... Read More about Airy Point Process at the liquid-gas boundary.

Limit distributions for KPZ growth models with spatially homogeneous random initial conditions (2018)
Journal Article
Chhita, S., Ferrari, P. L., & Spohn, H. (2018). Limit distributions for KPZ growth models with spatially homogeneous random initial conditions. Annals of Applied Probability, 28(3), 1573-1603. https://doi.org/10.1214/17-aap1338

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... Read More about Limit distributions for KPZ growth models with spatially homogeneous random initial conditions.

A combinatorial identity for the speed of growth in an anisotropic KPZ model (2017)
Journal Article
Chhita, S., & Ferrari, P. L. (2017). A combinatorial identity for the speed of growth in an anisotropic KPZ model. Annales de l’Institut Henri Poincaré D, 4(4), 453-477. https://doi.org/10.4171/aihpd/45

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 Toninell... Read More about A combinatorial identity for the speed of growth in an anisotropic KPZ model.

Domino statistics of the two-periodic Aztec diamond (2016)
Journal Article
Chhita, S., & Johansson, K. (2016). Domino statistics of the two-periodic Aztec diamond. Advances in Mathematics, 294, 37-149. https://doi.org/10.1016/j.aim.2016.02.025

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.... Read More about Domino statistics of the two-periodic Aztec diamond.

Asymptotic domino statistics in the Aztec diamond (2015)
Journal Article
Chhita, S., Johansson, K., & Young, B. (2015). Asymptotic domino statistics in the Aztec diamond. Annals of Applied Probability, 25(3), 1232-1278. https://doi.org/10.1214/14-aap1021

We study random domino tilings of the Aztec diamond with different weights for horizontal and vertical dominoes. A domino tiling of an Aztec diamond can also be described by a particle system which is a determinantal process. We give a relation betwe... Read More about Asymptotic domino statistics in the Aztec diamond.

Tacnode GUE-minor processes and double Aztec Diamonds (2014)
Journal Article
Adler, M., Chhita, S., Johansson, K., & van Moerbeke, P. (2014). Tacnode GUE-minor processes and double Aztec Diamonds. Probability Theory and Related Fields, 162(1), 275-325. https://doi.org/10.1007/s00440-014-0573-9

We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, t... Read More about Tacnode GUE-minor processes and double Aztec Diamonds.

Coupling functions for domino tilings of Aztec diamonds (2014)
Journal Article
Chhita, S., & Young, B. (2014). Coupling functions for domino tilings of Aztec diamonds. Advances in Mathematics, 259, 173-251. https://doi.org/10.1016/j.aim.2014.01.023

The inverse Kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics. In this paper, we consider three different weightin... Read More about Coupling functions for domino tilings of Aztec diamonds.

The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid (2012)
Journal Article
Chhita, S. (2012). The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid. Journal of Statistical Physics, 148(1), 67-88. https://doi.org/10.1007/s10955-012-0529-3

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In the thermo... Read More about The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid.