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From random matrices to free groups, through non-crossing partitions
 

Summary: From random matrices to free groups,
through non-crossing partitions
Michael Anshelevich
March 4, 2002
RANDOM MATRICES
For each N, A(N), B(N) = independent N N sym-
metric Gaussian random matrices, i.e. A
(N)
ij = A
(N)
ji ,
otherwise independent Gaussian N(0, 1
N ).
Arise in: nuclear physics, quantum chaos, communica-
tion theory, string theory.
Want joint moments
1
N
Tr[p1(A(N))q1(B(N)) . . . pk(A(N))qk(B(N))].
Example .

  

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

 

Collections: Mathematics