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Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures

math.PR · 2025-07-29 · conditional · novelty 8.0

For fixed-q q-Racah tilings of a large hexagon, the 2D Gibbs measure collapses to a random 1D barcode staircase; the paper proves exponential concentration to a deterministic waterfall profile and conjectures the limiting kernel.

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  • Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures math.PR · 2025-07-29 · conditional · none · ref 2012

    For fixed-q q-Racah tilings of a large hexagon, the 2D Gibbs measure collapses to a random 1D barcode staircase; the paper proves exponential concentration to a deterministic waterfall profile and conjectures the limiting kernel.