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
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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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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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