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Kalikow's 0-1 conjecture for directional escape in random environments
Kalikow's 0-1 conjecture.
openergodic-theory random-walks-in-random-environments
06
The deterministic limiting velocity conjecture for stationary ergodic random environments
Let $(X_n)_{n\geq 0}$ be a random walk in a stationary ergodic environment on $\mathbb{Z}^d$ . A deterministic limiting velocity is a vector $v$ such that … for almost every realisa…
openergodic-theory law-of-large-numbers random-walks-in-random-environments
05
The transience-condition $(T)$ conjecture for strongly mixing random environments
The transience-condition $(T)$ conjecture. Directional transience along an open set $\mathcal U_{\ell}$ is equivalent to condition $(T)|\ell$ .
openballisticity probability random-walks-in-random-environments
04
Conjectured distributional limit for the quenched CLT error in one-dimensional random environments
Distributional-limit conjecture. If $\kappa\in(2,3)$ , then
openhitting-times quenched-central-limit-theorem random-walks-in-random-environments
06