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Grounded Lipschitz functions on trees are typically flat

   
@article{ECP2796,
	author = {Ron Peled and Wojciech Samotij and Amir Yehudayoff},
	title = {Grounded Lipschitz functions on trees are typically flat},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {Random Lipschitz functions; rooted trees},
	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.},
	pages = {no. 55, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2796},    
        url = {http://ecp.ejpecp.org/article/view/2796}}