Geodesic
Path counting and random matrix theory
The electronic journal of combinatorics, Tome 10 (2003)
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We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the $\beta$-Hermite and $\beta$-Laguerre ensembles of random matrix theory. We conclude by presenting two other identities obtained in the same way, for which finding combinatorial proofs is an open problem.
DOI : 10.37236/1736
Classification : 05A19, 15B52, 82B41
Mots-clés : identities, Dyck paths, Motzkin paths, random walks, random matrix 
@article{10_37236_1736,
     author = {Ioana Dumitriu and Etienne Rassart},
     title = {Path counting and random matrix theory},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1736},
     zbl = {1031.05017},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1736/}
}
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Ioana Dumitriu; Etienne Rassart. Path counting and random matrix theory. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1736

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