Representations of stack triangulations in the plane

Preprint English OPEN
Selig, Thomas (2013)
  • Subject: Mathematics - Probability | 60C05

Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these random stack triangulations in the plane $\R^2$ and study the asymptotic properties of these drawings, viewed as random compact metric spaces. We also look at the occupation measure of the vertices, and show that for these two distributions it converges to some random limit measure.
  • References (14)
    14 references, page 1 of 2

    [1] M. Albenque and J.-F. Marckert. Some families of increasing planar maps. Electron. J. Probab., 13:no. 56, 1624{1671, 2008.

    [2] D. Aldous. Cambridge University Press, 1991.

    [3] D. Aldous. Tree-based models for random distribution of mass. J. Stat. Phys, 73:625{641, 1993.

    [4] D. Aldous. Recursive self-similarity for random trees, random triangulations and brownian excursion. The Annals of Probability, 22(2):pp. 527{545, 1994.

    [5] J. Barral. Moments, continuite, et analyse multifractale des martingales de mandelbrot. Probability Theory and Related Fields, 113:535{569, 1999.

    [6] P. Billingsley. Probability and measure. 3rd ed. Chichester: John Wiley & Sons Ltd., 1995.

    [7] N. Bonichon, S. Felsner, and M. Mosbah. Convex drawings of 3-connected plane graphs. Algorithmica, 47(4):399{420, 2007.

    [8] D. Burago, Y. Burago, and S. Ivanov. A course in metric geometry. Providence, RI: American Mathematical Society (AMS), 2001.

    [9] N. Curien and I. Kortchemski. Random non-crossing plane con gurations: A conditioned galton-watson tree approach. 2012.

    [10] E. Fekete. Branching random walks on binary search trees: convergence of the occupation measure. ESAIM, Probab. Stat., 14:286{298, 2010.

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