Summary.
We study the asymptotic behaviour of disconnection and non-intersection exponents for planar Brownian motionwhen the number of considered paths tends to infinity. In particular, if η n (respectively ξ (n, p)) denotes the disconnection exponent for n paths (respectively the non-intersection exponent for n paths versus p paths), then we show that lim n →∞ η n /n = 1 2 and that for a > 0 and b > 0,lim n →∞ ξ ([na],[nb])/n = (√ a + √ b) 2 /2.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 28 February 1996 / In revised form: 3 September 1996
Rights and permissions
About this article
Cite this article
Werner, W. Asymptotic behaviour of disconnection and non-intersection exponents. Probab Theory Relat Fields 108, 131–152 (1997). https://doi.org/10.1007/s004400050104
Issue Date:
DOI: https://doi.org/10.1007/s004400050104