Dynkin, E. B. Self-intersection gauge for random walks and for Brownian motion. (English) Zbl 0638.60081 Ann. Probab. 16, No. 1, 1-57 (1988). 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. Reviewer: J.Le Gall Cited in 26 Documents MSC: 60J65 Brownian motion 60G60 Random fields 60J55 Local time and additive functionals 60G50 Sums of independent random variables; random walks Keywords:multiple points of planar random walks; self-intersections of a planar Brownian motion; renormalized self-intersection local times PDFBibTeX XMLCite \textit{E. B. Dynkin}, Ann. Probab. 16, No. 1, 1--57 (1988; Zbl 0638.60081) Full Text: DOI