Length spectrum of large genus random metric maps
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 ex...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000313/type/journal_article |
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| author | Simon Barazer Alessandro Giacchetto Mingkun Liu |
| author_facet | Simon Barazer Alessandro Giacchetto Mingkun Liu |
| author_sort | Simon Barazer |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-ed73d30cb53740b4913b4f8d693c805e |
| institution | OA Journals |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-ed73d30cb53740b4913b4f8d693c805e2025-08-20T02:11:33ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.31Length spectrum of large genus random metric mapsSimon Barazer0Alessandro Giacchetto1https://orcid.org/0000-0001-8415-5066Mingkun Liu2https://orcid.org/0009-0003-4116-9881Université Paris-Saclay, CNRS, IHES, 35 routes de Chartres, Bures-sur-Yvette, F-91440, France; E-mail:Departement Mathematik, ETH Zürich, Rämisstrasse 101, Zürich, CH-8044, Switzerland; E-mail:DMATH, FSTM, University of Luxembourg, 6 avenue de la Fonte, Esch-sur-Alzette, L-4365, LuxembourgWe 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.https://www.cambridge.org/core/product/identifier/S2050509425000313/type/journal_article05C1005C8032G1557M50 |
| spellingShingle | Simon Barazer Alessandro Giacchetto Mingkun Liu Length spectrum of large genus random metric maps Forum of Mathematics, Sigma 05C10 05C80 32G15 57M50 |
| title | Length spectrum of large genus random metric maps |
| title_full | Length spectrum of large genus random metric maps |
| title_fullStr | Length spectrum of large genus random metric maps |
| title_full_unstemmed | Length spectrum of large genus random metric maps |
| title_short | Length spectrum of large genus random metric maps |
| title_sort | length spectrum of large genus random metric maps |
| topic | 05C10 05C80 32G15 57M50 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000313/type/journal_article |
| work_keys_str_mv | AT simonbarazer lengthspectrumoflargegenusrandommetricmaps AT alessandrogiacchetto lengthspectrumoflargegenusrandommetricmaps AT mingkunliu lengthspectrumoflargegenusrandommetricmaps |