TY - JOUR
T1 - Random anti-commuting Hermitian matrices
AU - McCarthy, John E.
AU - McCarthy, Hazel T.
N1 - Publisher Copyright:
© 2024 World Scientific Publishing Company.
PY - 2024/10/1
Y1 - 2024/10/1
N2 - We consider pairs of anti-commuting 2p-by-2p Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of 2-by-2 blocks on which the first matrix has eigenvalues }xj and the second has eigenvalues }yj. We call {(xj, yj )} the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling..
AB - We consider pairs of anti-commuting 2p-by-2p Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of 2-by-2 blocks on which the first matrix has eigenvalues }xj and the second has eigenvalues }yj. We call {(xj, yj )} the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling..
KW - Random matrix tuples
KW - anti-commuting matrices
UR - http://www.scopus.com/inward/record.url?scp=85199908788&partnerID=8YFLogxK
U2 - 10.1142/S2010326324500199
DO - 10.1142/S2010326324500199
M3 - Article
AN - SCOPUS:85199908788
SN - 2010-3263
VL - 13
JO - Random Matrices: Theory and Application
JF - Random Matrices: Theory and Application
IS - 4
M1 - 2450019
ER -