Electronic Journal of Probability

Limits of sequences of Markov chains

Henry Towsner

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Markov chain graph limit ultraproduct

This work is licensed under aCreative Commons Attribution 3.0 License.


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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