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Loop-free Markov chains as determinantal point processes

Borodin, Alexei (2008) Loop-free Markov chains as determinantal point processes. Annales De l'Institut Henri Poincaré - Probabilitiés et Statistiques, 44 (1). pp. 19-28. ISSN 0246-0203. doi:10.1214/07-aihp115.

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We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.

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Additional Information:© Association des Publications de l’Institut Henri Poincaré, 2008. Received 1 June 2006; accepted 25 September 2006. This research was partially supported by the NSF grant DMS-0402047 and the CRDF grant RIM1-2622-ST-04. The author would also like to thank the referees for a number of valuable suggestions.
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Subject Keywords:Markov chain; Determinantal point process
Issue or Number:1
Classification Code:Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G55: Point processes
Record Number:CaltechAUTHORS:20180809-133557869
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Official Citation:Borodin, Alexei. Loop-free Markov chains as determinantal point processes. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 1, 19--28. doi:10.1214/07-AIHP115.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88708
Deposited By: George Porter
Deposited On:09 Aug 2018 20:56
Last Modified:16 Nov 2021 00:29

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