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Sub-ballistic random walk in Dirichlet environment

   
@article{EJP2109,
	author = {Élodie Bouchet},
	title = {Sub-ballistic random walk in Dirichlet environment},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {18},
	year = {2013},
	keywords = {Random walk in random environment; Dirichlet distribution; Reinforced random walks; Invariant measure viewed from the particle},
	abstract = { 
We consider random walks in Dirichlet environment (RWDE) on $\mathbb{Z} ^d$, for $d \geq 3$, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, \dots, \alpha _{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We prove that the continuous-time accelerated walk has an absolutely continuous invariant probability measure for the environment viewed from the particle. This allows to characterize directional transience for the initial RWDE. It solves as a corollary the problem of Kalikow's $0-1$ law in the Dirichlet case in any dimension. Furthermore, we find the polynomial order of the magnitude of the original walk's displacement.
},
	pages = {no. 58, 1-25},
	issn = {1083-6489},
	doi = {10.1214/EJP.v18-2109},    
        url = {http://ejp.ejpecp.org/article/view/2109}}