Semicircular families of general covariance from Wigner matrices with permuted entries
Semicircular families of general covariance from Wigner matrices with permuted entries
Abstract Let $$(\sigma _N^{(i)})_{i \in I}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mi>N</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>i</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>I</mml:mi> </mml:mrow> </mml:msub> </mml:math> be a family of symmetric permutations of the entries of a Wigner matrix $${\mathbf {W}}_N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>N</mml:mi> </mml:msub> …