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Jiahao Chen
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Why only three classical matrix ensembles in RMT? (Newbie question)

I am just starting out on understanding random matrix theory from a background in applied mathematics. I have a very basic question about the Gaussian ensembles: why are there only three classical Gaussian ensembles? This seems very mysterious to me. Is it historically motivated from applications, or is there a deeper reason? I thought it might arise from exhausting all possible classes of diagonalizable matrices of a certain symmetry, but I have no idea if this is true or not.

I haven't been able to find a good expository reference for this, so any thoughts along those lines are also welcome.

Jiahao Chen
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  • 31