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Research Article

Some properties of exponential trees

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Pages 16-32 | Received 12 Jan 2021, Accepted 16 Aug 2021, Published online: 12 Sep 2021

References

  • A. Barabási and R. Albert, Emergence of scaling in random networks, Science 286 (1999), pp. 509–512.
  • P. Billingsley, Probability and Measure, Anniversary Ed., Wiley, Hoboken, NJ, 2012.
  • M. Drmota, Random Trees: An Interplay Between Combinatorics and Probability, Springer-Verlag Wien, New York, NY, 2009.
  • Y. Feng and H. Mahmoud, Profile of random exponential binary trees, Method. Comput. Appl. Probab.20 (2018), pp. 575–587.
  • A. Frieze and M. Karoński, Introduction to Random Graphs, 2nd Ed., Cambridge University Press, Cambridge, UK, 2016.
  • R. Grübel and Z. Kabluchko, Edgeworth expansions for profiles of lattice branching random walks, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53 (2017), pp. 2103–2134.
  • M. Hofri and H. Mahmoud, Algorithmics of Nonuniformity: Tools and Paradigms, CRC Press, Boca Raton, FL, 2018.
  • Z. Kabluchko, A. Marynych, and H. Sulzbach, General edgeworth expansions with applications to profiles of random trees, Ann. Appl. Probab. 27 (2017), pp. 347835–347924.
  • H. Kesten and B. Stigum, Limit theorems for decomposable multi-dimensional Galton-Watson processes, J. Math. Anal. Appl. 17 (1967), pp. 309–338.
  • T. Kurtz, R. Lyons, R. Pemantle, and Y. Peres, A Conceptual Proof of the Kesten-Stigum Theorem for Multi-type Branching Processes, in Classical and modern branching processes, Proceedings of the IMA workshop, Minneapolis, MN, USA. Springer, New York, 1997, pp. 181–185.
  • H. Mahmoud, Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021.
  • A. Meir and J. Moon, On the altitude of nodes in random trees, Can. J. Math. 30 (1978), pp. 997–1015.
  • R. Smythe, H. Mahmoud, and J. Szymański, On the structure of plane-oriented recursive trees and their branches, Random Struct. Algorithms 4 (1993), pp. 151–176.
  • R. Smythe and H. Mahmoud, A survey of recursive trees, Theor. Probab. Math. Stat. 51 (1995), pp. 1–27.

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