Random Dirichlet environment viewed from the particle in dimension d≥3

• Autores: Christophe Sabot
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 2, 2013, págs. 722-743
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Zd, RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d≥3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result and from [Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 1–8] a complete description of the ballistic regime for d≥3.