Electronic Communications in Probability

Uniform bounds for exponential moment of maximum of a Dyck path

Oleksiy Khorunzhiy and Jean-François Marckert

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 32, 327-333.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234741

Digital Object Identifier
doi:10.1214/ECP.v14-1486

Mathematical Reviews number (MathSciNet)
MR2535080

Zentralblatt MATH identifier
1189.60023

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60G70: Extreme value theory; extremal processes 60F99: None of the above, but in this section

Keywords
Dyck paths Bernoulli bridge random matrices

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Khorunzhiy, Oleksiy; Marckert, Jean-François. Uniform bounds for exponential moment of maximum of a Dyck path. Electron. Commun. Probab. 14 (2009), paper no. 32, 327--333. doi:10.1214/ECP.v14-1486. https://projecteuclid.org/euclid.ecp/1465234741


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