this talk is a report on joint work with s. molchanov. one set of results involves the behavior of sums of the form $\sum_{i=1}^{n(n)}\exp{\beta(\sum_{i=1}^n v_{ij}}$ where $v_{ij}$ are iid random variables. we identify rates of growth of $n(n)$ which give stable limit laws for properly normalized and centered sums, and other rates which give rise to a central limit theorem holding for these sums. another aspect of the work, which is related, considers sums of the form $\sum_{x \in q_{l(n)}} u(n,x)$, where the function $u(t,x)$ is the solution of parabolic anderson model and $q_l$ is a box in $z^d$ of radius l. again the limit behavior of such sums depends on the rate of growth of $l(n)$. the results for this setting give a relation between intermittency and the so-called quenched-to-annealed transition.