Uniform bounds for exponential moment of maximum of a Dyck paths

Details Uniform bounds for exponential moment of maximum of a Dyck paths Uniform bounds for exponential moment of maximum of a Dyck paths

2009-02-07

arxiv.org/abs/0902.1229v2

Mathematics

Probability

7 pages; accepted by Electronic Communications in Probability

Scientific paper

Let D be a Dyck path chosen uniformly from the set of Dyck paths with 2n steps. We prove that the sequence of the exponential moments of the maximum of D normalized by the square root of n converges in the limit of infinite n, and therefore is bounded uniformly in n. This result justifies corresponding assumption used to prove certain estimates of high moments of large random matrices.

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