Random Planar Lattices and Integrated SuperBrownian Excursion

@inproceedings{Schaeffer2002RandomPL,
  title={Random Planar Lattices and Integrated SuperBrownian Excursion},
  author={Gilles Schaeffer},
  year={2002}
}
In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous’ Integrated SuperBrownian Excursion (ISE). As a consequence, the radius rn of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r = R−L of the support of the one-dimensional ISE, or precisely: n−1/4rn law −→ (8/9) r. More generally the distribution of distances to a random vertex in a random quadrangulation is described… CONTINUE READING
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