Examples of Condition $(T)$ for Diffusions in a Random Environment
Tom Schmitz, ETH Zurich
Abstract
With the help of the methods developed in our previous article [Schmitz, to appear in Annales de l'I.H.P., in press], we highlight condition $(T)$ as a source of new examples of 'ballistic' diffusions in a random environment when d>1 ('ballistic' means that a strong law of large numbers with non-vanishing limiting velocity holds).
In particular we are able to treat the case of non-constant diffusion coefficients,
a feature that causes problems.
Further we
recover the ballistic character of two important classes of diffusions in a random environment
by simply checking condition $(T)$.
This not only points out to the broad range of examples where condition $(T)$ can
be checked, but
also fortifies our belief that
condition $(T)$ is a natural contender for the characterisation of ballistic diffusions in a random environment when d>1.
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