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Critical large deviations of one-dimensional annealed Brownian motion in a Poissonian potential
We derive a large deviation principle for the position at large times $t$ of a one-dimensional annealed Brownian motion in a Poissonian potential in the critical spatial scale $t^{1/3}$. Here “annealed” means that averages are taken with respect to both the path and environment measures. In contrast to the $d$-dimensional …