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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 448, Pages 252–262
(Mi znsl6315)
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Asymptotics of the Jordan normal form of a random nilpotent matrix
F. V. Petrova, V. V. Sokolovb a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Abstract:
We study the Jordan normal form of an upper triangular matrix constructed from a random acyclic graph or a random poset. Some limit theorems and concentration results for the number and sizes of Jordan blocks are obtained. In particular, we study a linear algebraic analog of Ulam's longest increasing subsequence problem.
Key words and phrases:
Jordan normal form, random poset, longest increasing subsequence, limit shape.
Received: 19.09.2016
Citation:
F. V. Petrov, V. V. Sokolov, “Asymptotics of the Jordan normal form of a random nilpotent matrix”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 252–262; J. Math. Sci. (N. Y.), 224:2 (2017), 339–344
Linking options:
https://www.mathnet.ru/eng/znsl6315 https://www.mathnet.ru/eng/znsl/v448/p252
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Abstract page: | 205 | Full-text PDF : | 60 | References: | 30 |
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