Electronic Journal of Probability

Limits of sequences of Markov chains

Henry Towsner

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Abstract

We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a convergent sequence of finite Markov chains with bounded mixing times a unique limit object: an infinite Markov chain with a measurable state space. The limits of the Markov chains we consider have discrete spectra, which makes the limit theory simpler than the general graph case, and illustrates how the discrete spectrum setting (sometimes called "random-free" or "product measurable") is simpler than the general case.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 77, 23 pp.

Dates
Accepted: 20 July 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067183

Digital Object Identifier
doi:10.1214/EJP.v20-4188

Mathematical Reviews number (MathSciNet)
MR3371436

Zentralblatt MATH identifier
1327.60148

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 03C20: Ultraproducts and related constructions

Keywords
Markov chain graph limit ultraproduct

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Towsner, Henry. Limits of sequences of Markov chains. Electron. J. Probab. 20 (2015), paper no. 77, 23 pp. doi:10.1214/EJP.v20-4188. https://projecteuclid.org/euclid.ejp/1465067183


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