Length spectrum of large genus random metric maps
Abstract 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.
Authors
- Simon Barazer
- Alessandro Giacchetto (ORCID: https://orcid.org/0000-0001-8415-5066)
- Mingkun Liu (ORCID: https://orcid.org/0009-0003-4116-9881)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Luxembourg (LU)
- Université Paris-Saclay (FR)
- ETH Zurich (CH)
- Institut des Hautes Études Scientifiques (FR)
Publication Details
- Journal
- Forum of Mathematics Sigma
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1017/fms.2025.31
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche