Abstract.
We consider the word associated to the homotopic class of the Brownian path (properly closed) in the thrice punctured sphere. We prove that its length has almost surely the same behaviour as a totally asymmetric Cauchy process on the line. More precisely, the liminf has the same normalization in t log(t) and the limsup can be described by the same integral test. They are the Brownian motion counterparts of some Lévy and Khintchine results on continued fraction expansions.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 17 December 1996 / Revised version: 23 February 1998
Rights and permissions
About this article
Cite this article
Gruet, JC. On the length of the homotopic Brownian word in the thrice punctured sphere. Probab Theory Relat Fields 111, 489–516 (1998). https://doi.org/10.1007/s004400050175
Issue Date:
DOI: https://doi.org/10.1007/s004400050175