### On the ballistic conjecture in RWRE

Probability Seminar

10th July 2020, 3:30 pm – 4:30 pm

online, https://zoom.us/j/93299847543

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.

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