Abstract
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.
| Translated title of the contribution | Déterminants de laplaciens sur les discrétisations de surfaces plates et torsion analytique. |
|---|---|
| Original language | English |
| Pages (from-to) | 743-751 |
| Number of pages | 9 |
| Journal | Comptes Rendus Mathematique |
| Volume | 358 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Jan 2020 |
| Externally published | Yes |