Fluctuations of random Motzkin paths

Włodzimierz Bryc; Yizao Wang

doi:10.1016/j.aam.2019.02.003

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arXiv · 1807.10057

Fluctuations of random Motzkin paths

Włodzimierz Bryc·Yizao Wang

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Abstract

It is known that after scaling a random Motzkin path converges to a Brownian excursion. We prove that the fluctuations of the counting processes of the ascent steps, the descent steps and the level steps converge jointly to linear combinations of two independent processes: a Brownian motion and a Brownian excursion. The proofs rely on the Laplace transforms and an integral representation based on an identity connecting non-crossing pair partitions and joint moments of an explicit non-homogeneous Markov process.

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Włodzimierz Bryc, Yizao Wang. 2018-07-26. Fluctuations of random Motzkin paths. https://doi.org/10.1016/j.aam.2019.02.003

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