## Electronic Communications in Probability

### Uniform bounds for exponential moment of maximum of a Dyck path

#### 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

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

Rights

#### 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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