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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 15 open journal systems 


Connected allocation to Poisson points in R2

Maxim Krikun, IECN, Universite Nancy 1


Abstract
This note answers one question in [1] concerning the connected allocation for the Poisson process in R2. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to the halfplane. A picture of a numerically simulated example is included.


Full text: PDF

Pages: 140-145

Published on: May 8, 2007
Bibliography
  1. C. Hoffman, A.E. Holroyd, Y. Peres. A stable marriage of Poisson and Lebesgue. Ann. Probab. 34 (2006), 1241--1272. Math. Review 2257646
  2. K.S. Alexander. Percolation and minimal spanning forests in infinite graphs. Ann. Probab. 23 (1995), 87--104. Math. Review 1330762
  3. S. Chatterjee, R. Peled, Y. Peres, D. Romik. Gravitational allocation to Poisson points (2006), math.PR/0611886
  4. R. Lyons, Y. Peres, O. Schramm. Minimal spanning forests. Ann. Probab. 34 (2006), 1665--1692. Math. Review 2271476
  5. D.E. Marshall, S. Rohde. Convergence of the zipper algorithm for conformal mapping (2006), math.CV/0605532
















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Electronic Communications in Probability. ISSN: 1083-589X