Uniform bounds for exponential moment of maximum of a Dyck path
Oleksiy Khorunzhiy, Université de Versailles, France
Jean-François Marckert, CNRS, LabRI, Université de Bordeaux
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 nis 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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