Current fluctuations in type-D ASEP
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For type-D ASEP with step initial data and fixed q, what is the limiting standardized current law of each species? The proposed marginal law is GUE Tracy–Widom F₂.
Why it matters and what counts as progress
Why it matters: A species-by-species result extends conjectures for small species counts through the model’s projected-current structure.
What counts as progress: A proof of each F₂ marginal with the scaling and autonomy identity explicit; marginal convergence alone does not determine the joint current law.
How the problem developed
- 26 Nov 2020 · Model construction [1]
Jeffrey Kuan, Mark Landry, Andrew Lin, Andrew Park and Zhengye Zhou Constructed a two-class type-D-symmetric interacting particle system and derived reversible measures and self-duality from quantum-group symmetry.
- 13 Jul 2026 · Reported asymptotic results [2]
Jeffrey Kuan, with Claude Opus 4.8 and Fable 5 Reported fixed-q current decoupling and Tracy–Widom fluctuations, plus weak-asymmetry limits with a nonzero correlation between the limiting random variables.
AI contribution
Correlated and uncorrelated long--time asymptotics of type D ASEP
For type-D ASEP with step initial data and fixed q, the standardized current of each species converges to the GUE Tracy–Widom F₂ law. Theorem 8.1 uses exact autonomy of each projected current and the known single-species step-ASEP limit.
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