Length spectrum of large genus random metric maps

Fuente: arXiv
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Main Authors: Barazer, Simon, Giacchetto, Alessandro, Liu, Mingkun
Format: Preprint
Published: 2023
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author Barazer, Simon
Giacchetto, Alessandro
Liu, Mingkun
author_facet Barazer, Simon
Giacchetto, Alessandro
Liu, Mingkun
contents We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case.
format Preprint
id arxiv_https___arxiv_org_abs_2312_10517
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Length spectrum of large genus random metric maps
Barazer, Simon
Giacchetto, Alessandro
Liu, Mingkun
Probability
Combinatorics
Geometric Topology
05C10, 05C80, 32G15, 57M50
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case.
title Length spectrum of large genus random metric maps
topic Probability
Combinatorics
Geometric Topology
05C10, 05C80, 32G15, 57M50
url https://arxiv.org/abs/2312.10517