The maximum relaxation time of a random walk
Combinatorics
2019-01-29 v2 Probability
Abstract
We show the minimum spectral gap of the normalized Laplacian over all simple, connected graphs on vertices is . This minimum is achieved asymptotically by a double kite graph. Consequently, this leads to sharp upper bounds for the maximum relaxation time of a random walk, settling a conjecture of Aldous and Fill. We also improve an eigenvalue-diameter inequality by giving a new lower bound for the spectral gap of the normalized Laplacian. This eigenvalue lower bound is asymptotically best possible.
Cite
@article{arxiv.1804.05500,
title = {The maximum relaxation time of a random walk},
author = {Sinan G. Aksoy and Fan Chung and Michael Tait and Josh Tobin},
journal= {arXiv preprint arXiv:1804.05500},
year = {2019}
}
Comments
This version is updated to address referee comments and will appear in Advances in Applied Mathematics