Random Walks in Random Environment

By Ofer Zeitouni. Encyclopedia of Complexity and Systems Science, 2009

476 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Branching random walks (2015, background): “indeed essentially borrowed from Solomon [224] for one-dimensional random walks in random environment.”
Positively and negatively excited random walks on integers, with branching processes (2008, result): “43 no.1, 195–199 [So75] F. Solomon (1975).”
A note on multitype branching processes with immigration in a random environment (2005, methodology): “The construction used in the proof is similar to that of L-safeguards for a RWRE introduced in [17], Section 3.”
Quenched invariance principle for random walks in balanced random environment (2010, methodology): “5 Transience in the general ergodic environment In this section we will prove (ii) of Theorem 1 by an argument similar to [19].”
A Quenched Invariance Principle for Certain Ballistic Random Walks in i.i.d. Environments (2007, unknown): “A version of Theorem 1.1 for d =2 , 3i spresented in Section 4. For d =1 , the conclusion of Theorem 1.1 does not hold, and a quenched invariance principle, or even a CLT, requires a different centering [ Zei04 , Gol07, Pet08].”