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.
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