Asymptotic behaviour of disconnection and non-intersection exponents |
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Authors: | Wendelin Werner |
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Institution: | (1) C.N.R.S. Laboratoire de Mathématiques, E.N.S., 45 rue d’Ulm, F-75230 Paris Cedex 05, France, e-mail: wwerner@dmi.ens.fr, FR |
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Abstract: | 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.
Received: 28 February 1996 / In revised form: 3 September 1996 |
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Keywords: | Mathematics Subject Classification (1991): 60J65 |
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