Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces
| dc.contributor.author | Gilmore, Clifford | |
| dc.contributor.author | Le Masson, Etienne | |
| dc.contributor.author | Sahlsten, Tuomas | |
| dc.contributor.author | Thomas, Joe | |
| dc.date.accessioned | 2021-04-30T09:08:04Z | |
| dc.date.available | 2021-04-30T09:08:04Z | |
| dc.date.issued | 2021-04-05 | |
| dc.description.abstract | We give upper bounds for Lp norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short geodesic loops passing through a point. When the genus g → +∞, we show that random hyperbolic surfaces X with respect to the WeilPetersson volume have with high probability at most one such loop of length less than c log g for small enough c > 0. This allows us to deduce that the Lp norms of L2 normalised eigenfunctions on X are O(1/√log g) with high probability in the large genus limit for any p > 2 +ε for ε > 0 depending on the spectral gap λ1(X) of X, with an implied constant depending on the eigenvalue and the injectivity radius. | en |
| dc.description.status | Peer reviewed | en |
| dc.description.version | Accepted Version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Gilmore, C., Le Masson, E., Sahlsten, T. and Thomas, J. (2021) 'Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces', Geometric and Functional Analysis, 31, pp. 62–110. doi: 10.1007/s00039-021-00556-6 | en |
| dc.identifier.doi | 10.1007/s00039-021-00556-6 | en |
| dc.identifier.eissn | 1420-8970 | |
| dc.identifier.endpage | 110 | en |
| dc.identifier.issn | 1016-443X | |
| dc.identifier.journaltitle | Geometric and Functional Analysis | en |
| dc.identifier.startpage | 62 | en |
| dc.identifier.uri | https://hdl.handle.net/10468/11239 | |
| dc.identifier.volume | 31 | en |
| dc.language.iso | en | en |
| dc.publisher | Springer Nature Switzerland AG | en |
| dc.rights | © 2021, The Authors, under exclusive licence to Springer Nature Switzerland AG, part of Springer Nature. This is a post-peer-review, pre-copyedit version of an article published in Geometric And Functional Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s00039-021-00556-6 | en |
| dc.subject | Lp | en |
| dc.subject | Eigenfunction | en |
| dc.subject | Laplacian | en |
| dc.subject | Short geodesic loops | en |
| dc.title | Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces | en |
| dc.type | Article (peer-reviewed) | en |
