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Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees
"... This paper provides tight bounds for the moments of the width of rooted labeled trees with n nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use one of the many one-to-one correspondences between trees and parking functions, and also a precise coupling between parking f ..."
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Cited by 18 (5 self)
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This paper provides tight bounds for the moments of the width of rooted labeled trees with n nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use one of the many one-to-one correspondences between trees and parking functions, and also a precise coupling between parking functions and the empirical processes of mathematical statistics. Our result turns out to be a consequence of the strong convergence of empirical processes to the Brownian bridge (Komlos, Major and Tusnady, 1975).
Extreme-value analysis of standardized gaussian increments. arXiv:0706.1849v2 [math.PR
, 2007
"... Let {Xi,i = 1,2,...} be i.i.d. standard gaussian variables. Let Sn = X1 +... + Xn be the sequence of partial sums and ..."
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Cited by 2 (0 self)
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Let {Xi,i = 1,2,...} be i.i.d. standard gaussian variables. Let Sn = X1 +... + Xn be the sequence of partial sums and
unknown title
, 903
"... Approximations for general bootstrap of empirical processes with an application to kernel-type density estimation ..."
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Approximations for general bootstrap of empirical processes with an application to kernel-type density estimation
