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Comparing the quenched and averaged large deviation rate functionsMathematical Physics & Probability
|Speaker: ||Atilla Yilmaz, UC Berkeley|
|Location: ||1147 MSB|
|Start time: ||Wed, Oct 21 2009, 4:10PM|
Consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. Denote the quenched and averaged rate functions
by $I_q$ and $I_a$, respectively. Note that $I_a$ is less than or equal to
$I_q$ by Jensen's inequality. Also, it is easy to see that $I_q$ and $I_a$
are not identically equal.
In this talk, I will present two results:
(1) For ballistic walks in dimensions four or more, $I_q$ and $I_a$ are
equal on a closed set whose interior contains every nonzero velocity at
which the rate functions vanish.
(2) The first result is not valid in general for ballistic walks in lower
dimensions. (Joint work with O. Zeitouni.)