New edge asymptotics of skew Young diagrams via free boundaries

D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.

Conference Paper | Published | English

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Author
Betea, Dan; Bouttier, Jérémie; Nejjar, PeterIST Austria; Vuletíc, Mirjana
Department
Abstract
We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.
Publishing Year
Date Published
2019-07-01
Proceedings Title
Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics
Acknowledgement
D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and to Alessandra Occelli for suggesting the name for the models of Section 2.
Article Number
34
Conference
FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics
Conference Location
Ljubljana, Slovenia
Conference Date
2019-07-01 – 2019-07-05
IST-REx-ID

Cite this

Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics; 2019.
Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.
Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019.
D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.
Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics
Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics, 2019.
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