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Random Boundary of a Planar Map

  • Maxim Krikun
  • Vadim Malyshev
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We consider the probability distribution PN on the class of neartriangulations T of the disk with N triangles, where each T is assumed to have the weight ym, m = mN = mN(T) is the number of boundary edges of T. We find the limiting distribution of the random variable mN(T) as N → ∞: in the critical point y = ycr = 6 the random variables NmN converge to a non-gaussian distribution , for y > ycr for some constant c the random variables N(mN - cN) converge to a gaussian distribution.

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References

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    V. Malyshev, 2001 Combinatorics and Probability of Maps. In ”Proceedings of the NATO Advanced Study Institute on Asymptotic Combinatorics in Mathematical Physics”. Kluwer (to appear).Google Scholar
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Maxim Krikun
    • 1
  • Vadim Malyshev
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.I.N.R.I.A.Le Chesnay CedexFrance

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