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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 onetoone correspondences between trees and parking functions, and also a precise coupling between parking f ..."
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Cited by 20 (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 onetoone 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).
Extremevalue analysis of standardized gaussian increments
, 2008
"... 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 5 (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 kerneltype density estimation ..."
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Approximations for general bootstrap of empirical processes with an application to kerneltype density estimation
Limiting Distributions for Sums of Independent Random Products
, 2009
"... Let {Xi,j: (i, j) ∈ N 2} be a twodimensional array of independent copies of a random variable X, and let {Nn}n∈N be a sequence of natural numbers such that limn→ ∞ e −cn Nn = 1 for some c> 0. Our main object of interest is the sum of independent random products ..."
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Let {Xi,j: (i, j) ∈ N 2} be a twodimensional array of independent copies of a random variable X, and let {Nn}n∈N be a sequence of natural numbers such that limn→ ∞ e −cn Nn = 1 for some c> 0. Our main object of interest is the sum of independent random products