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Asymptotic behaviour of disconnection and non-intersection exponents
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  • Published: May 1997

Asymptotic behaviour of disconnection and non-intersection exponents

  • Wendelin Werner1 

Probability Theory and Related Fields volume 108, pages 131–152 (1997)Cite this article

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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.

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  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

    Wendelin Werner

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  1. Wendelin Werner
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Received: 28 February 1996 / In revised form: 3 September 1996

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Werner, W. Asymptotic behaviour of disconnection and non-intersection exponents. Probab Theory Relat Fields 108, 131–152 (1997). https://doi.org/10.1007/s004400050104

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  • Issue Date: May 1997

  • DOI: https://doi.org/10.1007/s004400050104

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  • Mathematics Subject Classification (1991): 60J65
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