  An overview is presented of recent work on some statistical problems on
multiparticle random walks. We consider a Euclidean, deterministic fractal or
disordered lattice and N >> 1 independent random walkers initially (t=0) placed
onto the same site of the substrate. Three classes of problems are considered:
(i) the evaluation of the average number <S_N(t)> of distinct sites visited
(territory explored) up to time t by the N random walkers, (ii) the statistical
description of the first passage time t_{j,N} to a given distance of the first
j random walkers (order statistics of exit times), and (iii) the statistical
description of the time \mathbf{t}_{j,N} elapsed until the first j random
walkers are trapped when a Euclidean lattice is randomly occupied by a
concentration c of traps (order statistics of the trapping problem). Although
these problems are very different in nature, their solutions share the same
form of a series in ln^{-n}(N) \ln^m \ln (N) (with n>=1 and 0<=m<=n) for N>>1.
These corrective terms contribute substantially to the statistical quantities
even for relatively large values of N.
