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2020 A polynomial upper bound for the mixing time of edge rotations on planar maps
Alessandra Caraceni
Electron. J. Probab. 25: 1-30 (2020). DOI: 10.1214/20-EJP519

Abstract

We consider a natural local dynamic on the set of all rooted planar maps with $n$ edges that is in some sense analogous to “edge flip” Markov chains, which have been considered before on a variety of combinatorial structures (triangulations of the $n$-gon and quadrangulations of the sphere, among others). We provide the first polynomial upper bound for the mixing time of this “edge rotation” chain on planar maps: we show that the spectral gap of the edge rotation chain is bounded below by an appropriate constant times $n^{-11/2}$. In doing so, we provide a partially new proof of the fact that the same bound applies to the spectral gap of edge flips on quadrangulations as defined in [8], which makes it possible to generalise the result of [8] to a variant of the edge flip chain related to edge rotations via Tutte’s bijection.

Citation

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Alessandra Caraceni. "A polynomial upper bound for the mixing time of edge rotations on planar maps." Electron. J. Probab. 25 1 - 30, 2020. https://doi.org/10.1214/20-EJP519

Information

Received: 14 January 2020; Accepted: 26 August 2020; Published: 2020
First available in Project Euclid: 25 September 2020

MathSciNet: MR4161128
Digital Object Identifier: 10.1214/20-EJP519

Subjects:
Primary: 60J10

JOURNAL ARTICLE
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