Bounds for the second largest eigenvalue of a transition matrix

Abstract

We find an upper bound, with general form, for the second largest eigenvalue of a transition matrix; special cases of which have previously been proposed as upper bounds and others which are new improvements.

Keywords:

• Cheeger constant
• nonmaximal eigenvalue
• transition matrix
• upper bound

Acknowledgement

The author is grateful to an anonymous referee for comments that have helped this article.