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Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves

hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
dc.contributor.authorDELECROIX, Vincent
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorGOUJARD, Élise
hal.structure.identifierEuler International Mathematical Institute [St. Petersburg]
dc.contributor.authorZOGRAF, Peter
hal.structure.identifierInstitut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
dc.contributor.authorZORICH, Anton
dc.date.accessioned2024-04-04T02:38:42Z
dc.date.available2024-04-04T02:38:42Z
dc.date.issued2022-10
dc.identifier.issn0020-9910
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190899
dc.description.abstractEnAbstract The volume $\mathcal {B}_{\Sigma }^{\textrm {comb}}({\mathbb {G}})$ of the unit ball—with respect to the combinatorial length function $\ell _{{\mathbb {G}}}$—of the space of measured foliations on a stable bordered surface $\Sigma $ appears as the prefactor of the polynomial growth of the number of multicurves on $\Sigma $. We find the range of $s \in {\mathbb {R}}$ for which $(\mathcal {B}_{\Sigma }^{\textrm {comb}})^{s}$, as a function over the combinatorial moduli spaces, is integrable with respect to the Kontsevich measure. The results depend on the topology of $\Sigma $, in contrast with the situation for hyperbolic surfaces where [6] recently proved an optimal square integrability.
dc.description.sponsorshipphysique mathématique - ANR-19-CE40-0021
dc.description.sponsorshipEspaces de modules de différentielles: surfaces plates et interactions - ANR-19-CE40-0003
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enLarge genus asymptotic geometry of random square-tiled surfaces and of random multicurves
dc.typeArticle de revue
dc.identifier.doi10.1007/s00222-022-01123-y
dc.subject.halMathématiques [math]
dc.identifier.arxiv2007.04740
bordeaux.journalInventiones Mathematicae
bordeaux.page123-224
bordeaux.volume230
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03862245
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03862245v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Inventiones%20Mathematicae&rft.date=2022-10&rft.volume=230&rft.issue=1&rft.spage=123-224&rft.epage=123-224&rft.eissn=0020-9910&rft.issn=0020-9910&rft.au=DELECROIX,%20Vincent&GOUJARD,%20%C3%89lise&ZOGRAF,%20Peter&ZORICH,%20Anton&rft.genre=article


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