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Random matrices The GUE Wigner's semi-circle law Harer-Zagier Largest and smallest eigenvalues Lecture I: Asymptotics for large GUE random
 

Summary: Random matrices The GUE Wigner's semi-circle law Harer-Zagier Largest and smallest eigenvalues
Lecture I: Asymptotics for large GUE random
matrices
Steen Thorbjørnsen, University of Aarhus
Random matrices The GUE Wigner's semi-circle law Harer-Zagier Largest and smallest eigenvalues
Random Matrices
Definition. Let (, F, P) be a probability space and let n be a
positive integer. Then a random n × n matrix A on (, F, P) is an
n × n-matrix
A = (aij )1i,jn,
where all the entries are complex valued random variables on
(, F, P). In other words, A is a measurable mapping
A: (, F, P) (Mn(C), B(Mn(C))),
when Mn(C) is equipped with its Borel -algebra B(Mn(C)).
Random matrices The GUE Wigner's semi-circle law Harer-Zagier Largest and smallest eigenvalues
The spectral distribution of a selfadjoint random
matrix
Let A: Mn(C) be a selfadjoint random matrix, i.e.,
A() = A() for all . Then for each we consider the ordered
eigenvalues

  

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

 

Collections: Mathematics