Random Boundary of a Planar Map
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 = 6-½ the random variables N-½mN converge to a non-gaussian distribution , for y > ycr for some constant c the random variables N-½(mN - cN) converge to a gaussian distribution.
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