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A simple derivation of Spitzer'z asymptotic law for Brownian windings[Trans.Am.Math.Soc.87,187 (1958)]is presented along with its generalizations>.These include the cases of planar Brownian walks interacting with a singlepuncture and Brownian walks on a single truncated cone with variable conicalangle interacting with the truncated conical tip.Such situations are typical inthe theories of quantum Hall effect and 2+1 quantum gravity, respectively .Theyalso have some applications in polymer physic

Elementary derivation of Spitzer’s asymptotic law for Brownian windings and some of its physical applications