  Be $X_t$ a random walk. We study its span $S$, i.e. the size of the domain
visited up to time $t$. We want to know the probability that $S$ reaches $1$
for the first time, as well as the density of the span given $t$. Analytical
results are presented, and checked against numerical simulations. We then
generalize this to include drift, and one or two reflecting boundaries. We also
derive the joint probability of the maximum and minimum of a process. Our
results are based on the diffusion propagator with reflecting or absorbing
boundaries, for which a set of useful formulas is derived.
