Area and Inertial Moment of Dyck Paths

Authors:
Michel Nguyen The
Affiliations:
Laboratoire d'Informatique de LIX, Ecole Polytechnique, 91128 Palaiseau Cedex, France (e-mail: mnguyen@lix.polytechnique.fr)
Venue:
Combinatorics, Probability and Computing
Year:
2004

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Abstract

In this paper, we investigate the limit law of the inertial moment of Dyck paths with respect to the $x$-axis, that is, the sum of the squares of the altitudes. We find its Laplace transform using Louchard's methodology, rediscovering a result which was in fact well known by probabilists. We give recurrence relations which enable us to compute the moments of the joint limit law of the area and the inertial moments of both Dyck paths and Grand Dyck paths (bilateral Dyck paths).