The bundle Laplacian on discrete tori
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 1, pp. 97-121.
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We prove an asymptotic formula for the determinant of the bundle Laplacian on discrete d-dimensional tori as the number of vertices tends to infinity. This determinant has a combinatorial interpretation in terms of cycle-rooted spanning forests. We also establish a relation (in the limit) between the spectral zeta function of a line bundle over a discrete torus, the spectral zeta function of the infinite graph ℤ d and the Epstein–Hurwitz zeta function. The latter can be viewed as the spectral zeta function of the twisted continuous torus which is the limit of the sequence of discrete tori.

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DOI : 10.4171/aihpd/66
Classification : 05-XX, 11-XX, 35-XX, 58-XX
Mots-clés : Bundle Laplacian, heat kernel, cycle-rooted spanning forest, spectral zeta function, Kronecker limit formula 
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     title = {The bundle {Laplacian} on discrete tori},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {97--121},
     volume = {6},
     number = {1},
     year = {2019},
     doi = {10.4171/aihpd/66},
     mrnumber = {3911691},
     zbl = {1407.05147},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/66/}
}
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Friedli, Fabien. The bundle Laplacian on discrete tori. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 1, pp. 97-121. doi : 10.4171/aihpd/66. http://archive.numdam.org/articles/10.4171/aihpd/66/

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