Penetration of hot electrons through a cold disordered wire

We study a penetration of an electron with high energy $E\gg T$ through strongly disordered wire of length $L\gg a$ ($a$ being the localization length). Such an electron can loose, but not gain the energy, when hopping from one localized state to another. We have found a distribution function for the transmission coefficient $\mathcal T$. The typical $\mathcal T$ remains exponentially small in $L/a$, but with the decrement, reduced compared to the case of direct elastic tunnelling: $\overline{\ln\mathcal T}\approx 0.237\cdot 2L/a$. The distribution function has a strong tail in the domain of anomalously high $\mathcal T$; the average $\overline{\mathcal T}\propto (a/L)^{2}$ is controlled by rare configurations of disorder, corresponding to this tail.