[Déterminants de laplaciens sur les discrétisations de surfaces plates et torsion analytique.]
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.
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@article{CRMATH_2020__358_6_743_0,
author = {Finski, Siarhei},
title = {Determinants of {Laplacians} on discretizations of flat surfaces and analytic torsion},
journal = {Comptes Rendus. Math\'ematique},
pages = {743--751},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {6},
year = {2020},
doi = {10.5802/crmath.94},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.94/}
}
TY - JOUR AU - Finski, Siarhei TI - Determinants of Laplacians on discretizations of flat surfaces and analytic torsion JO - Comptes Rendus. Mathématique PY - 2020 SP - 743 EP - 751 VL - 358 IS - 6 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.94/ DO - 10.5802/crmath.94 LA - en ID - CRMATH_2020__358_6_743_0 ER -
%0 Journal Article %A Finski, Siarhei %T Determinants of Laplacians on discretizations of flat surfaces and analytic torsion %J Comptes Rendus. Mathématique %D 2020 %P 743-751 %V 358 %N 6 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.94/ %R 10.5802/crmath.94 %G en %F CRMATH_2020__358_6_743_0
Finski, Siarhei. Determinants of Laplacians on discretizations of flat surfaces and analytic torsion. Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 743-751. doi : 10.5802/crmath.94. http://www.numdam.org/articles/10.5802/crmath.94/
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