{"id":"palomar/PALOMAR-2026-10-30-000007","url":"https://github.com/igor-kortchemski/total-variation-threshold-parking-functions/tree/f5daa3e5871a3d9e9c853334ca5b2e528f2309aa","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-30-000007-v1.json","repo":"https://github.com/igor-kortchemski/total-variation-threshold-parking-functions","tags":["math.PR","math.CO","msc:60C05","msc:60F05"],"score":0,"title":"Parking functions: total variation threshold and critical profile","trust":"high","domain":"math.PR","source":"palomar","authors":["Igor Kortchemski"],"reviews":0,"subject":"math.PR","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-30","reactions":{},"formalized":true,"formalizes":[{"title":"A total variation threshold for the first coordinates of uniform parking functions via Lorentzian polynomials","identifier":"https://arxiv.org/abs/2610.40082v1","relationship":"formalizes"}]}