The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory

A new approach is presented for the study of the probability that the random paths generated by two independent Brownian motions in ^d intersect or, more generally, are within a short distancea of each other. The well known behavior of that function ofa-above, below, and at the critical dimensiond=4, as well as further corrections, are derived here by means of a single renormalization group equation. The equation's derivation is expected to shed some light on the -function of the _d⁴ quantum field theory.Sloan Foundation Research Fellow. Research supported in part by NSF grant PHY-8301493