The Gamma-Disordered Aztec Diamond

par Maurice Duits

jeudi 21 mai 2026, 15:30 → 16:30 Europe/Paris

435 (ENS de Lyon)

The Aztec diamond is a central exactly solvable model in probability and combinatorics. Its striking geometric features — most notably limit shapes and arctic boundaries — have made it a cornerstone of integrable probability. Over the past decade, weighted variants with doubly periodic edge weights have shown that much of this integrable structure persists well beyond the uniform case. These extensions have revealed new phenomena, including regions of smooth disorder, and are governed by a remarkable birational transformation that encodes the algebraic structure of the model After a brief survey of these developments, I will present recent joint work with Roger Van Peski on a new disordered version of the Aztec diamond, obtained by assigning independent Gamma-distributed weights to its edges. Despite the randomness in the weights, the model retains enough algebraic structure to remain integrable. This allows us to rigorously identify new disorder-driven behavior, including n^{2/3)-scale fluctuations near the turning points of the arctic boundary. These turning points are closely related to certain integrable polymer models.