Height and diameter of brownian tree

Article, Preprint, Other literature type English OPEN
Wang, Minmin;
(2015)
  • Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
  • Journal: issn: 1083-589X
  • Related identifiers: doi: 10.1214/ECP.v20-4193
  • Subject: Brownian tree | Williams' decomposition | Brownian excursion | continuum random tree | [MATH]Mathematics [math] | Jacobi theta function | [ MATH ] Mathematics [math] | [MATH] Mathematics [math] | Mathematics - Probability | 60J80 | Williams’ decomposition | [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
    arxiv: Mathematics::Probability

International audience; By computations on generating functions, Szekeres proved in 1983 that the law of the diameter of a uniformly distributed rooted labelled tree with n vertices, rescaled by a factor n −1/2 , converges to a distribution whose density is explicit. Al... View more
  • References (23)
    23 references, page 1 of 3

    [1] Romain Abraham and Jean-François Delmas, Williams' decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations, Stochastic Process. Appl. 119 (2009), no. 4, 1124-1143. MR-2508567

    [2] David Aldous, The continuum random tree. I, Ann. Probab. 19 (1991), no. 1, 1-28. MR1085326

    [3] , The continuum random tree. II. An overview, Stochastic analysis (Durham, 1990), London Math. Soc. Lecture Note Ser., vol. 167, Cambridge Univ. Press, Cambridge, 1991, pp. 23-70. MR-1166406

    [4] , The continuum random tree. III, Ann. Probab. 21 (1993), no. 1, 248-289. MR-1207226

    [5] David Aldous and Jim Pitman, Tree-valued Markov chains derived from Galton-Watson processes, Ann. Inst. H. Poincaré Probab. Statist. 34 (1998), no. 5, 637-686. MR-1641670

    [6] Jean Bertoin, Lévy processes, Cambridge Tracts in Mathematics, vol. 121, Cambridge University Press, Cambridge, 1996. MR-1406564

    [7] Robert M. Blumenthal, Excursions of Markov processes, Probability and its Applications, Birkhäuser Boston, Inc., Boston, MA, 1992. MR-1138461

    [8] Andrei N. Borodin and Paavo Salminen, Handbook of Brownian motion-facts and formulae, Probability and its Applications, Birkhäuser Verlag, Basel, 1996. MR-1477407

    [9] Nicolas Broutin and Philippe Flajolet, The distribution of height and diameter in random nonplane binary trees, Random Structures Algorithms 41 (2012), no. 2, 215-252. MR-2956055

    [10] Kai Lai Chung, Excursions in Brownian motion, Ark. Mat. 14 (1976), no. 2, 155-177. MR0467948

  • Metrics
    No metrics available
Share - Bookmark