Random walkers absorbed at a boundary — the first-passage time follows a Lévy stable distribution with heavy tail.
For a 1D Brownian motion starting at x=0 with absorbing boundary at x=L, the first-passage time PDF is the inverse Gaussian (Wald distribution): p(t) = L/√(2πt³) · exp(−(L−μt)²/(2t)). With μ=0, this is a Lévy distribution p(t) ∝ t^(−3/2) — a heavy-tailed distribution with divergent mean (if drift=0). With positive drift, the mean is L/μ.