Universal inequalities for Dirichlet eigenvalues on discrete groups

Bobo Hua; Ariel Yadin

doi:10.4171/JST/498

Universal inequalities for Dirichlet eigenvalues on discrete groups

Bobo Hua
, Ariel Yadin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary condition on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, Pólya, 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).

Original language	English
Pages (from-to)	933-957
Number of pages	25
Journal	Journal of Spectral Theory
Volume	14
Issue number	3
DOIs	https://doi.org/10.4171/JST/498
State	Published - 1 Jan 2024

Keywords

Cayley graphs
Laplacian eigenvalues on graphs
universal inequalities

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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10.4171/JST/498

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title = "Universal inequalities for Dirichlet eigenvalues on discrete groups",

abstract = "We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary condition on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, P{\'o}lya, 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).",

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AB - We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary condition on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, Pólya, 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).

KW - Cayley graphs

KW - Laplacian eigenvalues on graphs

KW - universal inequalities

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Universal inequalities for Dirichlet eigenvalues on discrete groups

Abstract

Keywords

ASJC Scopus subject areas

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