Diffusive decay of the environment viewed by the particle. (English) Zbl 1321.60216

Summary: We prove an optimal diffusive decay of the environment viewed by the particle in a random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach of A. Gloria et al. [Invent. Math. 199, No. 2, 455–515 (2015; Zbl 1314.39020)], is very short and elementary.


60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60J27 Continuous-time Markov processes on discrete state spaces
76M50 Homogenization applied to problems in fluid mechanics


Zbl 1314.39020
Full Text: DOI arXiv