English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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. Résumé. 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. Funding. This work is supported by the European Research Council grant ALKAGE number 670846 managed by Jean-Pierre Demailly. Manuscript received 7th January 2020, accepted 29th June 2020.

Determinants of Laplacians on discretizations of flat surfaces and analytic torsion