Asymptotics of the generating function for the volume of the Wiener sausage

Michiel van den Berg, Erwin Bolthausen

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We consider the generating function {Mathematical expression} of the voltime of the Wiener sausage C?(t), which is the e-neighbourhood of the Wiener path in the time interval [0, t]. For ?<0, the limiting behavior for t?8, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For ?>0 it had been investigated by van den Berg and Tóth, but in contrast to the case ?<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large ?. © 1984 Springer-Verlag.

Original languageEnglish
Pages (from-to)389-397
Number of pages9
JournalProbability Theory and Related Fields
Issue number3
Publication statusPublished - Sept 1994


  • Mathematics Subject Classification (1994): 60J65, 60F10, 60J45


Dive into the research topics of 'Asymptotics of the generating function for the volume of the Wiener sausage'. Together they form a unique fingerprint.

Cite this