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Antonia H¨ ofert, Jonas Jalowy, Zakhar Kabluchko,Zeros of polynomial powers under the heat flow, arXiv preprint ( · 2025 · arXiv 2512.17808

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P\'olya--Schur problems and free probability

math.PR · 2026-05-29 · unverdicted · novelty 8.0

Any free additive infinitely divisible distribution is the weak limit of root distributions of Appell polynomials f_n(∂_z)z^n for Laguerre-Pólya sequences f_n, with extensions to multiplicative cases, rectangular convolution, and limiting Cauchy distribution for Jensen polynomials of the Riemann Xi-

The Rectangular Finite Free Heat Flow

math.PR · 2026-06-05 · unverdicted · novelty 6.0

Introduces and studies the rectangular finite free heat flow as a dynamical system on polynomials with equivalent characterizations, root asymptotics, and connections to Calogero-Moser systems and mean curvature flow on Lie group orbits.

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  • P\'olya--Schur problems and free probability math.PR · 2026-05-29 · unverdicted · none · ref 47

    Any free additive infinitely divisible distribution is the weak limit of root distributions of Appell polynomials f_n(∂_z)z^n for Laguerre-Pólya sequences f_n, with extensions to multiplicative cases, rectangular convolution, and limiting Cauchy distribution for Jensen polynomials of the Riemann Xi-

  • The Rectangular Finite Free Heat Flow math.PR · 2026-06-05 · unverdicted · none · ref 29

    Introduces and studies the rectangular finite free heat flow as a dynamical system on polynomials with equivalent characterizations, root asymptotics, and connections to Calogero-Moser systems and mean curvature flow on Lie group orbits.