Bose–Einstein-like condensation of deformed random matrix: a replica approach
Bose–Einstein-like condensation of deformed random matrix: a replica approach
Abstract In this work, we investigate a symmetric deformed random matrix, which is obtained by perturbing the diagonal elements of the Wigner matrix. The eigenvector <?CDATA $\boldsymbol{x}_\mathrm{min}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi mathvariant="bold-italic">x</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> </mml:msub> </mml:math> of the minimal eigenvalue <?CDATA $\lambda_\mathrm{min}$?> <mml:math …