English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a random walk in a random environment on $\mathbb{Z}^d$ underSznitman's ballisticity condition $(T)$. Using techniques from arXiv:1405.6819,we show the existence of the invariant measure $Q$ with respect to theenvironment viewed from the particle for $d=2$ and $d=3$. This disproves aconjecture made in arXiv:1405.6819 that the invariant measure does not exist indimension $2$. As a corollary, we prove sharp tail bounds for regenerationtimes for $d=3$. Finally, we also provide tail estimates for the Radon-Nikodymderivative $dQ/dP$, where $P$ is the original distribution on the environment.

Environment Viewed from the Particle and Slowdown Estimates for Ballistic RWRE on $\mathbb{Z}^2$ and $\mathbb{Z}^3$