Work

Regular hyperbolic tilings have no $\ell^2$ eigenfunctions

Year: 2026

Type: preprint

Abstract: We show that the adjacency operator of the $1$-skeleton of any regular tiling of the hyperbolic plane has no nonzero square-integrable eigenfunctions. As a consequence, the same holds for every infinite connected regular graph admitting a proper planar embedding with regular dual.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11857

Author: Nachmias, Asaf

Institution: Tel Aviv University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Israel Science Foundation, Simons Institute for the Theory of Computing, University of California Berkeley, H2020 European Research Council

Award: Universality of random planar maps and trees

OpenAlex ID: W7212292419

Cites:

Cited by: 1

Related to: 10