The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk

We identify the limit of the internal DLA cluster generated by Sinai's walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law.

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Bibliographische Detailangaben
Veröffentlicht in:	Annales de l'I.H.P. Probabilités et statistiques 2010-11, Vol.46 (4), p.991-1000
Hauptverfasser:	ENRIQUEZ, N, LUCAS, C, SIMENHAUS, F
Format:	Artikel
Sprache:	eng
Schlagworte:	60F05 60K37 Exact sciences and technology Excursion theory General topics Internal DLA Mathematics Probability Probability and statistics Probability theory and stochastic processes Random walks in random environments Sciences and techniques of general use Sinai’s walk Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Statistics Stochastic processes
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Beschreibung
Zusammenfassung:	We identify the limit of the internal DLA cluster generated by Sinai's walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law.
ISSN:	0246-0203 1778-7017
DOI:	10.1214/09-AIHP336