Random laminations and multitype branching processes

Nicolas Curien (DMA Ens Paris)
Yuval Peres (Microsoft Research Redmond)

Abstract


We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination process of [1]. The proofs use the infinite dimensional Perron-Frobenius theory and quasi-stationary distributions.

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Pages: 435-446

Publication Date: August 19, 2011

DOI: 10.1214/ECP.v16-1641

References

  1. N. Curien and J.-F. Le Gall. Random recursive triangulations of the disk via fragmentation theory. Annals of Probab. (to appear) Math. Review number not available.
  2. A.N. Kolmogorov. Zur lšsung einer biologischen aufgabe [german: On the solution of a problem in biology]. Izv. NII Matem. Mekh. Tomskogo Univ., 2:7--12, 1938. Math. Review number not available.
  3. E. Seneta and D. Vere-Jones. On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. J. Appl. Probability, 3:403--434, 1966. 0207047
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