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Correlated and uncorrelated long--time asymptotics of type D ASEP

Jeffrey Kuan

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.

Sources for this record

What was already known

The type-D model and dualities came from earlier human work. F₂ marginals were conjectured for n=2,3, and the single-species step-ASEP limit was already known.

AI involvement AI-led

Kuan reports that Claude Opus 4.8 and Fable 5 wrote the mathematical body and proofs, with later Claude corrections to two §6 lemmas. The human author wrote the abstract and introduction and supplied the earlier model and research context.

The first-person disclosure assigns the proof-bearing mathematical body to Claude models, while Kuan guided the project and manually checked it.

Importance Notable

Extends the marginal law to every species through a decoupling identity.

Limitations

The fixed-q cross-current covariance asymptotic remains a conjecture. The reported Lean counterpart has explicit stochastic-process interface assumptions.

Technical verification Formal (Lean 4 + human)

Kuan reports a complete manual proof check. The paper also reports a Lean formalization with named hypothesis bundles for foundational stochastic-process interfaces; the exact Lean theorem-to-paper correspondence was not rebuilt here.

Formal checking

Manual verification of the paper’s proofs

Checker
Jeffrey Kuan, paper author
Scope
Theorem 8.1 Tracy–Widom marginal convergence under the stated step and fixed-q assumptions
Basis
Reported by the linked checker

Formalization over Mathlib, no sorry for theorem statements, with dependency graph and compiled declarations reported

Checker
Lean 4 formalization built with Aristotle and Claude
Scope
Theorem 8.1 formal counterpart and its dependencies; process-existence interfaces remain explicit hypotheses where used
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Full

Kuan explains that each species projection is an autonomous ASEP, making the fixed-q marginal convergence a transfer of the established single-species result.

Correction and publication history