Self-intersection gauge for random walks and for Brownian motion (Q1099505)

This paper presents very general limit theorems connecting classes of random fields associated with multiple points of planar random walks and functionals associated with self-intersections of a planar Brownian motion. These limit theorems allow the author to recover the existence and main properties of the so-called renormalized self-intersection local times of planar Brownian motion, which he had introduced in previous papers [see, e.g., Regularized self-intersection local times of planar Brownian motion, ibid. 16, 58-74 (1988)]. The concluding section of the present paper contains a survey of the existing literature on Brownian self-intersections, a subject which has been growing extensively during the last years.