Geodesic
Asymptotics of the Jordan normal form of a random nilpotent matrix
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 252-262 
F. V. Petrov; V. V. Sokolov. Asymptotics of the Jordan normal form of a random nilpotent matrix. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 252-262. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a16/
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     author = {F. V. Petrov and V. V. Sokolov},
     title = {Asymptotics of the {Jordan} normal form of a~random nilpotent matrix},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a16/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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