TY - JOUR
T1 - Spectral properties of the Jacobi ensembles via the Coulomb gas approach
AU - Ramli, Huda Mohd
AU - Katzav, Eytan
AU - Castillo, Isaac Pérez
PY - 2012/11/23
Y1 - 2012/11/23
N2 - Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices in the limit of large matrices. This allows us to derive the rate functions for the large fluctuations to the left and the right of the expected values of the smallest and largest eigenvalues analytically. Our findings are compared with some available known exact results as well as with numerical simulations finding good agreement.
AB - Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices in the limit of large matrices. This allows us to derive the rate functions for the large fluctuations to the left and the right of the expected values of the smallest and largest eigenvalues analytically. Our findings are compared with some available known exact results as well as with numerical simulations finding good agreement.
UR - http://www.scopus.com/inward/record.url?scp=84868355136&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/45/46/465005
DO - 10.1088/1751-8113/45/46/465005
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AN - SCOPUS:84868355136
SN - 1751-8113
VL - 45
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 46
M1 - 465005
ER -