Loop-free Markov chains as determinantal point processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, p. 19-28

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.

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.

DOI : https://doi.org/10.1214/07-AIHP115
Classification:  60J10,  60G55
Keywords: Markov chain, determinantal point process
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     author = {Borodin, Alexei},
     title = {Loop-free Markov chains as determinantal point processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {1},
     year = {2008},
     pages = {19-28},
     doi = {10.1214/07-AIHP115},
     zbl = {pre05610822},
     mrnumber = {2451569},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_1_19_0}
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Borodin, Alexei. Loop-free Markov chains as determinantal point processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, pp. 19-28. doi : 10.1214/07-AIHP115. http://www.numdam.org/item/AIHPB_2008__44_1_19_0/

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