Comptes Rendus
no. 6
Probabilité, Géométrie différentielle, Analyse globale sur les variétés
Determinants of Laplacians on discretizations of flat surfaces and analytic torsion
[Déterminants de laplaciens sur les discrétisations de surfaces plates et torsion analytique.]
Siarhei Finski1
1 Institut Fourier - Université Grenoble Alpes, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 743-751.

Nous étudions le développement asymptotique des déterminants de laplaciens des graphes associés aux discrétisations d’une surface de demi-translation munie d’un fibré vectoriel hermitien plat. Ainsi, sur les discrétisations, nous mettons en relation les déterminants zêta-régularisés avec le développement asymptotique du nombre d’arbres couvrants et la fonction de partition des forêts couvrantes d’unicycles d’un poids déterminé par la monodromie de la connexion unitaire du fibré vectoriel hermitien.

We study the asymptotic expansion of the determinants of the graph Laplacians associated to discretizations of a half-translation surface endowed with a unitary flat vector bundle. By doing so, over the discretizations, we relate the asymptotic expansion of the number of spanning trees and the partition function of cycle-rooted spanning forests, weighted by the monodromy of the unitary connection of the vector bundle, to the corresponding zeta-regularized determinants.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.94

Siarhei Finski 1

1 Institut Fourier - Université Grenoble Alpes, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Siarhei Finski. Determinants of Laplacians on discretizations of flat surfaces and analytic torsion. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 743-751. doi : 10.5802/crmath.94. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.94/

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