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2009 Uniform bounds for exponential moment of maximum of a Dyck path
Oleksiy Khorunzhiy, Jean-François Marckert
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Electron. Commun. Probab. 14: 327-333 (2009). DOI: 10.1214/ECP.v14-1486


Let us consider the maximum $M(D)$ of a Dyck path $D$ chosen uniformly in the set of Dyck paths with $2n$ steps. We prove that the exponential moment of $M(D)$ normalized by the square root of $n$ is bounded in the limit of infinite $n$. This uniform bound justifies an assumption used in literature to prove certain estimates of high moments of large random matrices.


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Oleksiy Khorunzhiy. Jean-François Marckert. "Uniform bounds for exponential moment of maximum of a Dyck path." Electron. Commun. Probab. 14 327 - 333, 2009.


Accepted: 12 August 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60023
MathSciNet: MR2535080
Digital Object Identifier: 10.1214/ECP.v14-1486

Primary: 60C05
Secondary: 60F99 , 60G70

Keywords: Bernoulli bridge , Dyck paths , random matrices

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