Geodesic
Expected size of a tree in the fixed point forest
Discrete mathematics & theoretical computer science, Permutation Patters 2018, Tome 21 (2019) no. 2.

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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. 
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     author = {Regan, Samuel and Slivken, Erik},
     title = {Expected size of a tree in the fixed point forest},
     journal = {Discrete mathematics & theoretical computer science},
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Regan, Samuel; Slivken, Erik. Expected size of a tree in the fixed point forest. Discrete mathematics & theoretical computer science, Permutation Patters 2018, Tome 21 (2019) no. 2. doi : 10.23638/DMTCS-21-2-1. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-2-1/

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