F. V. Petrov, V. V. Sokolov, “Asymptotics of the Jordan normal form of a random nilpotent matrix”, Zap. Nauchn. Sem. POMI, 2016, Volume 448,Pages <nobr>252

Asymptotics of the Jordan normal form of a random nilpotent matrix

F. V. Petrov^a, V. V. Sokolov^b

^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.

UDC: 519.172.3+519.179.4+519.212.2+512.643

Received: 19.09.2016