Defines (n,d)-rectangular cumulants that linearize (n,d)-rectangular convolution in finite free probability and converge to q-rectangular free cumulants as d→∞ with 1+n/d→q.
Kabluchko, Lee-Yang zeroes of the Curie-Weiss ferromagnet, unitary Hermite polynomials, and the backward heat flow, arXiv:2203.05533 [math.PR]
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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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Cumulants in rectangular finite free probability and beta-deformed singular values
Defines (n,d)-rectangular cumulants that linearize (n,d)-rectangular convolution in finite free probability and converge to q-rectangular free cumulants as d→∞ with 1+n/d→q.
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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.