Reuse distance is a basic metric for program locality. The
distribution of reuse distances, called the reuse signature, shows the average locality or the amount of actively used
data. Random access is often assumed in analytical models
about program behavior. An interesting question is whether
the reuse behavior of random data access has a closed-form
answer. We prove that the length of reuse distances of random access is uniformly distributed from 0 to n-1; 1 when n is the size of data.
For further reference please refer his MSPC'08 position paper.