A generalized Cheeger inequality and the Steklov Problem on finite graphs
Differential Geometry
2025-09-09 v1 Probability
Abstract
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Cheeger inequalities for Steklov eigenvalues. In particular, we get a sharp estimate for the first non-trivial Steklov eigenvalue via Escobar Cheeger constant. At the end, we extend Hassannezhad and Miclo's convergence result to non-reversible Markov chains via a different method based on resolvent convergence, answering one of their questions.
Cite
@article{arxiv.2509.05667,
title = {A generalized Cheeger inequality and the Steklov Problem on finite graphs},
author = {Bobo Hua and Supanat Kamtue and Shiping Liu and Florentin Münch and Norbert Peyerimhoff},
journal= {arXiv preprint arXiv:2509.05667},
year = {2025}
}