Geodesic
Tree/endofunction bijections and concentration inequalities
Steven Heilman1
1University of Southern California Mathematics
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings $f\colon\{1,\ldots,n\}\to\{1,\ldots,n\}$ and doubly rooted trees on $n$ vertices. The main application is a concentration inequality for the number of vertices connected to an independent set in a uniformly random tree, which is then used to prove partial unimodality of its independent set sequence. So, we give probabilistic arguments for inequalities that often use combinatorial arguments.
DOI : 10.37236/10560
Classification : 60C05, 60F05, 05C05, 05C80
Mots-clés : concentration inequalities, uniformly random trees

Steven Heilman  1

1 University of Southern California Mathematics 
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Steven Heilman. Tree/endofunction bijections and concentration inequalities. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10560

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