@inproceedings{3885a58fe6464242921bfbff303038f5,
title = "Faster Triangulation Mixing via Transport Flows",
abstract = "We prove an Oe(n2) bound for the relaxation time and the log-Sobolev time (inverse log-Sobolev constant) of the classical triangulation flip chain on a convex (n + 2)-gon, implying a mixing time of Oe(n2). The previous state of the art for the mixing time of this chain due to Eppstein and Frishberg [20] was Oe(n3), while the best known lower bound on the mixing time due to Molloy, Reed and Steiger [36] is Ω(n3/2). Our relaxation time bound makes significant progress towards Aldous' [3] conjectured bound of Θ(n3/2) for the relaxation time. We improve upon the analysis of [20] by further developing the framework of transport flows introduced in the work [13] of Chen et al. In this light, our results can be seen as a more efficient way of using combinatorial decompositions to obtain functional inequalities for Markov chains. We hope our ideas will find other applications in the future.",
keywords = "log-Sobolev inequality, Markov chain, MCMC, mixing time, multicommodity flow, random walk, spectral gap, transport flow, triangulations",
author = "Alev, \{Vedat Levi\} and Daniel Frishberg and Michail Sarantis and Prasad Tetali",
note = "Publisher Copyright: {\textcopyright} Vedat Levi Alev, Daniel Frishberg, Michail Sarantis, and Prasad Tetali.; 53rd International Colloquium on Automata, Languages, and Programming, ICALP 2026 ; Conference date: 07-07-2026 Through 10-07-2026",
year = "2026",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2026.12",
language = "אנגלית",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Sayan Bhattacharya and Danupon Nanongkai and Michael Benedikt and Gabriele Puppis",
booktitle = "53rd International Colloquium on Automata, Languages, and Programming, ICALP 2026",
address = "גרמניה",
}