## Kyoto Journal of Mathematics

### Cover times for sequences of reversible Markov chains on random graphs

Yoshihiro Abe

#### Abstract

We provide conditions that classify sequences of random graphs into two types in terms of cover times. One type (type $1$) is the class of random graphs on which the cover times are of the order of the maximal hitting times scaled by the logarithm of the size of vertex sets. The other type (type $2$) is the class of random graphs on which the cover times are of the order of the maximal hitting times. The conditions are described by some parameters determined by random graphs: the volumes, the diameters with respect to the resistance metric, and the coverings or packings by balls in the resistance metric. We apply the conditions to and classify a number of examples, such as supercritical Galton–Watson trees, the incipient infinite cluster of a critical Galton–Watson tree, and the Sierpinski gasket graph.

#### Article information

Source
Kyoto J. Math., Volume 54, Number 3 (2014), 555-576.

Dates
First available in Project Euclid: 14 August 2014

https://projecteuclid.org/euclid.kjm/1408020878

Digital Object Identifier
doi:10.1215/21562261-2693442

Mathematical Reviews number (MathSciNet)
MR3263552

Zentralblatt MATH identifier
1338.60181

#### Citation

Abe, Yoshihiro. Cover times for sequences of reversible Markov chains on random graphs. Kyoto J. Math. 54 (2014), no. 3, 555--576. doi:10.1215/21562261-2693442. https://projecteuclid.org/euclid.kjm/1408020878

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