Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Loop-free Markov chains as determinantal point processes

Alexei Borodin

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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.

Résumé

Nous montrons que toute chaîne de Markov sans cycles sur un espace discret peut être vue comme un processus ponctuel determinantal. Comme application, nous démontrons des théorèmes limites centrales pour le nombre de particules dans une fenêtre pour des processus de renouvellement et des processus de renouvellement markoviens avec un bruit de Bernoulli.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 1 (2008), 19-28.

Dates
First available in Project Euclid: 25 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1203969866

Digital Object Identifier
doi:10.1214/07-AIHP115

Mathematical Reviews number (MathSciNet)
MR2451569

Zentralblatt MATH identifier
1186.60066

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G55: Point processes

Keywords
Markov chain Determinantal point process

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


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