Samuel Regan ; Erik Slivken - Expected size of a tree in the fixed point forest

dmtcs:5331 - Discrete Mathematics & Theoretical Computer Science, September 27, 2019, Vol. 21 no. 2, Permutation Patters 2018 - https://doi.org/10.23638/DMTCS-21-2-1
Expected size of a tree in the fixed point forestArticle

Authors: Samuel Regan ; Erik Slivken

    We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process configuration on $[0,1]^\mathbb{N}$. We generalize this random tree, and compute the expected size and expected number of leaves of a random rooted subtree in the generalized version. We also obtain bounds on the variance of the size.


    Volume: Vol. 21 no. 2, Permutation Patters 2018
    Published on: September 27, 2019
    Accepted on: September 10, 2019
    Submitted on: March 30, 2019
    Keywords: Mathematics - Probability,60C05
    Funding:
      Source : OpenAIRE Graph
    • A mathematical approach to the liquid-glass transition: kinetically constrained models, cellular automata and mixed order phase transitions; Funder: European Commission; Code: 680275

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