Geometric Bounds for Eigenvalues of Markov Chains
The work
| Authors | Persi W. Diaconis; Daniel W. Stroock |
|---|---|
| Editors | |
| Type | article |
| Year | 1991 |
| Citekey | diaconis1991geometric |
Where it appeared
| Published in | The Annals of Applied Probability |
|---|---|
| Publisher | Institute of Mathematical Statistics |
| Volume | 1 |
| Issue | 1 |
| Pages | 36--61 |
Identifiers
| DOI | 10.1214/aoap/1177005980 |
|---|---|
| OpenAlex | W2043694962 |
Access
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Abstract
We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering number of associated graphs. The bounds compare well with exact answers for a variety of simple chains and seem better than bounds derived through Cheeger-like inequalities. They offer improved rates of convergence for the random walk associated to approximate computation of the permanent.
How it got here
| How it got here | agent via openalex |
|---|---|
| Added | 2026-10-27 08:49 UTC |
| Not denied by | a person 2026-10-29 17:12 UTC |
Cite it as
@article{diaconis1991geometric,
title = {Geometric Bounds for Eigenvalues of Markov Chains},
author = {Persi W. Diaconis and Daniel W. Stroock},
year = {1991},
journal = {The Annals of Applied Probability},
publisher = {Institute of Mathematical Statistics},
volume = {1},
number = {1},
pages = {36--61},
doi = {10.1214/aoap/1177005980},
}
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