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. https://resolver.caltech.edu/CaltechAUTHORS:20180809-133557869
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Abstract
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.
Item Type: | Article | |||||||||
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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 | |||||||||
DOI: | 10.1214/07-aihp115 | |||||||||
Record Number: | CaltechAUTHORS:20180809-133557869 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180809-133557869 | |||||||||
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. https://projecteuclid.org/euclid.aihp/1203969866 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 88708 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | George Porter | |||||||||
Deposited On: | 09 Aug 2018 20:56 | |||||||||
Last Modified: | 16 Nov 2021 00:29 |
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