Open Research Index

Parking functions: total variation threshold and critical profile

Igor Kortchemski

Palomar Registrypalomar/PALOMAR-2026-10-30-000007Oct 30, 2026math.PRscore 0

A Lean formalization of the total variation threshold for initial coordinates of a uniform parking function. The three recorded results give uniform finite-size bounds, the Gaussian critical profile at scale n/log n (including zero and infinite parameters), and a quantitative relative-entropy and total-variation comparison with independent marginals. The library reconstructs the supplied manuscript through Borel marginal asymptotics, homogeneous log-concavity and entropy methods. It also proves the separate Pitman–Stanley volume-polynomial remark. The results concern probabilists and…

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