Global Asymptotics of Jack-Deformed Random Young Diagrams via Lukasiewicz Paths

Explore a 50-minute conference talk on the global asymptotics of Jack-deformed random Young diagrams using Lukasiewicz paths. Delve into discrete analogues of one-dimensional log-gas systems with N particles in a potential V at inverse temperature ß ≥ 0. Discover universal formulas describing global asymptotics of two discrete ß-ensemble models in high, low, and fixed-temperature regimes. Examine the surprising positivity properties expressed through weighted lattice paths like Motzkin, Dyck, and Lukasiewicz paths. Investigate the limit shape in high/low-temperature regimes and uncover the phase transition phenomenon when moving from fixed-temperature to high/low-temperature regimes. Gain insights from Maciej Dolega's presentation at IPAM's Integrability and Algebraic Combinatorics Workshop, based on joint work with Cesar Cuenca and Alex Moll.