Universal inequalities for Dirichlet eigenvalues on discrete groups
Differential Geometry
2020-07-28 v1 Group Theory
Probability
Abstract
We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary conditions on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, Polya, Yau, and others. Here we focus on a version by Cheng and Yang. Specifically, we prove Yang-type universal inequalities for Cayley graphs of finitely generated amenable groups, as well as for the d-regular tree (simple random walk on the free group).
Cite
@article{arxiv.2007.13157,
title = {Universal inequalities for Dirichlet eigenvalues on discrete groups},
author = {Bobo Hua and Ariel Yadin},
journal= {arXiv preprint arXiv:2007.13157},
year = {2020}
}