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Bouchet, Élodie; Ramírez, Alejandro F.; Sabot, Christophe

Sharp ellipticity conditions for ballistic behavior of random walks in random environment. (English) Zbl 1337.60249

Bernoulli 22, No. 2, 969-994 (2016).
Authors’ abstract: We sharpen ellipticity criteria for random walks in i.i.d. random environments introduced by D. Campos and A. F. Ramírez [Probab. Theory Relat. Fields 160, No. 1–2, 189–251 (2014; Zbl 1306.60151)] which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of N. Berger et al. [Commun. Pure Appl. Math. 67, No. 12, 1947–1973 (2014; Zbl 1364.60140)]. As a corollary, we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension \(d=2\) under which the corresponding random walk is ballistic.
Reviewer: Marius Iosifescu (Bucureşti)

Cited in 4 Documents

MSC:

60K37 Processes in random environments
60G50 Sums of independent random variables; random walks

Keywords:

random walks; random environments; ellipticity conditions; ballistic behavior; Dirichlet distribution; max-flow min-cut theorem

Citations:

Zbl 1306.60151; Zbl 1364.60140
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\textit{É. Bouchet} et al., Bernoulli 22, No. 2, 969--994 (2016; Zbl 1337.60249)
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References:

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