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Grounded Lipschitz functions on trees are typically flat


 
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1. Title Title of document Grounded Lipschitz functions on trees are typically flat
 
2. Creator Author's name, affiliation, country Ron Peled; Tel Aviv University; Israel
 
2. Creator Author's name, affiliation, country Wojciech Samotij; Tel Aviv University; Israel
 
2. Creator Author's name, affiliation, country Amir Yehudayoff; Technion-IIT; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Lipschitz functions; rooted trees
 
3. Subject Subject classification 05C60; 60C05; 82B41
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-07-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2796
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2796
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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