Asymptotics of zeta determinants of Laplacians on large degree abelian covers

2025/05/02 by Dang, Nguyen Viet, Lin, Jiasheng, Naud, Frédéric · 1 citation
#58C40 58J50 58J52 11M36 81T20 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2505.01586

Abstract

Let (M,g) be some smooth, closed, compact Riemannian manifold and (M_N↦ M)_N be an increasing sequence of large degree cyclic covers of M that converges when N→ +∞, in a suitable sense, to some limit ℤ^p cover M_∞ over M. Motivated by recent works on zeta determinants on random surfaces and some natural questions in Euclidean quantum field theory, we show the convergence of the sequence \fraclogdet_ζ(Δ_N)Vol(M_N) when N→ +∞ where Δ_N is the Laplace-Beltrami operator on M_N. We also generalize our results to the case of twisted Laplacians coming from certain flat unitary vector bundles over M.

Citations

• The moduli space of twisted Laplacians and random matrix theory
• The Bayes Principle and Segal Axioms for P(ϕ)₂, with application to Periodic Covers
• Determinants of Laplacians on random hyperbolic surfaces
• Simplicial spanning trees in random Steiner complexes
• Covariant Schrödinger semigroups on Riemannian manifolds
• Spectral deviations for the damped wave equation

Cited by

• Constructive Quantum Field Theory on Curved Surfaces and Related Topics

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