Limiting root distribution after repeated fractional differentiation is the push-forward of the initial distribution under a characteristic flow of the log-potential PDE.
C., Ho, C.-W.: The heat flow conjecture for random matric es
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Derives coupled SDEs for eigenvalue and eigenvector-overlap processes in non-Hermitian Brownian motion and SPDEs for the regularized FK determinant random field.
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Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators
Limiting root distribution after repeated fractional differentiation is the push-forward of the initial distribution under a characteristic flow of the log-potential PDE.
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Eigenvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion
Derives coupled SDEs for eigenvalue and eigenvector-overlap processes in non-Hermitian Brownian motion and SPDEs for the regularized FK determinant random field.