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Some images related to my research interests

Code for generating images provided by Christophe Charlier through his website.

Uniform tiling of the Aztec diamond and the arctic circle theorem, see [3]

Tiling with i.i.d. standard lognormal weights, conjectured to display a super-rough region, see [5]

Model with layered randomness, i.e. weights periodic in one direction, but otherwise log-normal distributed, see [1], [4].

Model with 2-periodic layered randomness, i.e. weights are 2-periodic in one direction and log-normal distributed otherwise.

Graph of the generalized discriminant (see [6]) associated to the 2x2-periodic model studied in [2]. Its zero-set is also known as the octic circle, as it is a degree 8 curve.

Literature

[1] A. Bufetov, L. Petrov and P. Zografos, Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions, arXiv:2507.08560

[2] S. Chhita and K. Johansson, Domino statistics of the two-periodic Aztec diamond, Adv. Math. 294, 37-149 (2016), doi.org/10.1016/j.aim.2016.02.025

[3] W. Jockusch, J. Propp and P. Shor, Random Domino Tilings and the Arctic Circle Theorem, arXiv:math/9801068

[4] Q. Moulard and F. Toninelli, Dimers with layered disorder, arXiv:2507.11964

[5] A. Perret, Z. Ristivojevic, P. Le Doussal, G. Schehr and K.J. Wiese, Super Rough Glassy Phase of the Random Field XY Model in Two Dimensions, Phys. Rev. Lett. 109, 157205 (2012), doi.org/10.1103/PhysRevLett.109.157205

[6] M. Piorkowski, Arctic curves of periodic dimer models and generalized discriminants, arXiv:2410.17138 (slides)

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