Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces

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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.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.volume 31 en
dc.identifier.startpage 62 en
dc.identifier.endpage 110 en
dc.identifier.issn 1016-443X
dc.identifier.uri http://hdl.handle.net/10468/11239
dc.identifier.doi 10.1007/s00039-021-00556-6 en
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.format.mimetype application/pdf 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
dc.internal.authorcontactother Clifford Gilmore, Mathematical Sciences, University College Cork, Cork, Ireland. T: +353-21- 490-3000 E: clifford.gilmore@ucc.ie en
dc.internal.availability Full text available en
dc.check.info Access to this article is restricted until 12 months after publication by request of the publisher. en
dc.check.date 2022-04-05
dc.description.version Accepted Version en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Geometric and Functional Analysis en
dc.internal.IRISemailaddress clifford.gilmore@ucc.ie en
dc.identifier.eissn 1420-8970


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