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2013 Grounded Lipschitz functions on trees are typically flat
Ron Peled, Wojciech Samotij, Amir Yehudayoff
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Electron. Commun. Probab. 18: 1-9 (2013). DOI: 10.1214/ECP.v18-2796

Abstract

A grounded $M$-Lipschitz function on a rooted $d$-ary tree is an integer valued map on the vertices that changes by at most $M$ along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their typical value at the root $v_0$ of the tree. We prove that the probability that the value of a uniformly chosen random function at $v_0$ is more than $M+t$ is doubly-exponentially small in $t$. We also show a similar bound for continuous (real-valued) grounded Lipschitz functions.

Citation

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Ron Peled. Wojciech Samotij. Amir Yehudayoff. "Grounded Lipschitz functions on trees are typically flat." Electron. Commun. Probab. 18 1 - 9, 2013. https://doi.org/10.1214/ECP.v18-2796

Information

Accepted: 6 July 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1298.05306
MathSciNet: MR3078018
Digital Object Identifier: 10.1214/ECP.v18-2796

Subjects:
Primary: 05C60
Secondary: 60C05, 82B41

JOURNAL ARTICLE
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