, Volume 96, Issue 5, pp 3455-3471

The law of large numbers and the central limit theorem for the jordan normal form of large triangular matrices over a finite field

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We define the Schur graph as the graph of shifted Young diagrams. Multiplicative central measures on this graph have a characteristic property: their transition probabilities differ from those of standard Plancherel's measures by a factor that depends on the added box and on the order of the diagram. We find all such measures and show that they are parametrized by one positive real number.

The author is pleased to thank A. A. Kirillov for posing the problem and for his attention to this work, and also S. V. Kerov and G. I. Olshanski for then: attention, helpful discussions, and support.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 18–43.
This work was supported by the International Soros Science Foundation and the International Soros Science Education Program.