Tohoku Mathematical Journal

Long time behavior of the transition probability of a random walk with drift on an abelian covering graph

Tomoyuki Shirai

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Abstract

For a certain class of reversible random walks possibly with drift on an abelian covering graph of a finite graph, using the technique of twisted transition operator, we obtain the asymptotic behavior of the $n$-step transition probability $p_n(x,y)$ as $n \to \infty$ and give an expression of the constant which appears in the asymptotics.

Article information

Source
Tohoku Math. J. (2) Volume 55, Number 2 (2003), 255-269.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113246940

Digital Object Identifier
doi:10.2748/tmj/1113246940

Mathematical Reviews number (MathSciNet)
MR1979498

Zentralblatt MATH identifier
1046.60044

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Citation

Shirai, Tomoyuki. Long time behavior of the transition probability of a random walk with drift on an abelian covering graph. Tohoku Math. J. (2) 55 (2003), no. 2, 255--269. doi:10.2748/tmj/1113246940. https://projecteuclid.org/euclid.tmj/1113246940.


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