Enrique Guerra

On the ballistic conjecture in RWRE

We start this talk by introducing with two dimensional examples the model of random walk in a random environment (RWRE). We then define several asymptotic terminology:
directional transience, ballisticity conditions and the ballistic regime. The definitions introduced will be sufficient for stating the main conjecture, delve into its connection with
the so-called (T) condition and explain in part why we expect an affirmative answer for
that open problem. In particular, we will see the relation between the nicknamed atypical
quenched estimate and ballistic behaviour. Finally, we will display some known results
which try to fill the gap needed to prove the ballistic conjecture. Results are joint work
with A. F. Ram´ırez, M. E. Vares and G. Valle.