{"ID":2872599,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.08560","arxiv_id":"2509.08560","title":"A transport approach to the cutoff phenomenon","abstract":"Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23; Sal24; Sal25a; PS25]. In the present paper, we propose an alternative approach which bypasses the use of varentropy and exploits instead a new W-TV transport inequality, combined with a classical parabolic regularization estimate [BGL01; OV01]. While currently restricted to non-negatively curved processes on smooth spaces, our argument no longer requires the chain rule, nor any approximate version thereof. As applications, we recover the main result of [Sal25a] establishing cutoff for the log-concave Langevin dynamics, and extend the conclusion to a widely-used discrete-time sampling algorithm known as the Proximal Sampler.","short_abstract":"Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23; Sal24; Sal25a; PS25]. In the present paper, we propose an alternative approach which bypasses the use of varentropy and exploits instead a...","url_abs":"https://arxiv.org/abs/2509.08560","url_pdf":"https://arxiv.org/pdf/2509.08560v2","authors":"[\"Francesco Pedrotti\",\"Justin Salez\"]","published":"2025-09-10T13:06:31Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.AP\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}