Intersection numbers of geodesic arcs

For a compact surface S with constant curvature -κ (for some and kappa 0) and genus g ≥ 2, we show that the tails of the distribution of the normalized intersection numbers i(α, β)/l(α)l(β) (where i(α, β) is the intersection number of the closed geodesics α and β and l(·) denotes the geometric lengt...