Law of Large Numbers for infinite random matrices over a finite field

  title={Law of Large Numbers for infinite random matrices over a finite field},
  author={Alexey Bufetov and Leonid Petrov},
  journal={Selecta Mathematica},
Asymptotic representation theory of general linear groups $$\hbox {GL}(n,F_\mathfrak {q})$$GL(n,Fq) over a finite field leads to studying probability measures $$\rho $$ρ on the group $$\mathbb {U}$$U of all infinite uni-uppertriangular matrices over $$F_\mathfrak {q}$$Fq, with the condition that $$\rho $$ρ is invariant under conjugations by arbitrary infinite matrices. Such probability measures form an infinite-dimensional simplex, and the description of its extreme points (in other words… 

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