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We study the probability distribution of residence time of a grain at a site,and its total residence time inside a pile, in different ricepile models. Thetails of these distributions are dominated by the grains that get deeply buriedin the pile. We show that, for a pile of size $L$, the probabilities that theresidence time at a site or the total residence time is greater than $t$, bothdecay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where$\gamma$ is an exponent $ \ge 1$, and values of $x$ and $\omega$ in the twocases are different. In the Oslo ricepile model we find that the probabilitythat the residence time $T_i$ at a site $i$ being greater than or equal to $t$,is a non-monotonic function of $L$ for a fixed $t$ and does not obey simplescaling. For model in $d$ dimensions, we show that the probability of minimumslope configuration in the steady state, for large $L$, varies as $\exp(-\kappaL^{d+2})$ where $\kappa$ is a constant, and hence $ \gamma = d+2$.Comment: 13 pages, 23 figures, Submitted to Phys. Rev.

Probability distribution of residence times of grains in models of rice piles