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Uniform bounds for exponential moment of maximum of a Dyck path

   
@article{ECP1486,
	author = {Oleksiy Khorunzhiy and Jean-François Marckert},
	title = {Uniform bounds for exponential moment of maximum of  a Dyck path},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {Dyck paths; Bernoulli bridge; random matrices},
	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.},
	pages = {no. 32, 327-333},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1486},    
        url = {http://ecp.ejpecp.org/article/view/1486}}