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Asymptotics of the Jordan Normal Form of a Random Nilpotent Matrix

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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.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

    F. V. Petrov

  2. St. Petersburg State Univeristy, St. Petersburg, Russia

    V. V. Sokolov

Authors
  1. F. V. Petrov
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  2. V. V. Sokolov
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Correspondence to F. V. Petrov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 252–262.

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Petrov, F.V., Sokolov, V.V. Asymptotics of the Jordan Normal Form of a Random Nilpotent Matrix. J Math Sci 224, 339–344 (2017). https://doi.org/10.1007/s10958-017-3419-z

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  • DOI: https://doi.org/10.1007/s10958-017-3419-z

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