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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 448, Pages 252–262 (Mi znsl6315)  
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
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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.
Funding agency Grant number
Saint Petersburg State University 6.38.223.2014
6.37.208.2016
Russian Foundation for Basic Research 14-01-00373a
Received: 19.09.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 2, Pages 339–344
DOI: https://doi.org/10.1007/s10958-017-3419-z
Bibliographic databases:
Document Type: Article
UDC: 519.172.3+519.179.4+519.212.2+512.643
Language: Russian
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
Citation in format AMSBIB
\Bibitem{PetSok16}
\by F.~V.~Petrov, V.~V.~Sokolov
\paper Asymptotics of the Jordan normal form of a~random nilpotent matrix
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 252--262
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6315}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3576262}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 339--344
\crossref{https://doi.org/10.1007/s10958-017-3419-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019661303}
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