---
res:
  bibo_abstract:
  - "In this work, we build a bridge between the Pólya--Schur program and Voiculescu's
    free probability theory. A cornerstone of the former is the Pólya--Benz Theorem,
    classifying a central family of real-root preserving operators on the space of
    polynomials, as those given by $f(\\partial_z)$ for a Laguerre--Pólya function
    $f$ and the derivative operator $\\partial_{z}$. We prove that any free (additive)
    infinitely divisible distribution can be attained as the weak limit of root distributions
    of Appell polynomials $f_n(\\partial_z)z^n$ as $n\\to\\infty$, for a suitably
    chosen sequence $f_n$ of Laguerre--Pólya functions.\r\n  Such questions on the
    (global) limiting distributions of real rooted polynomials belong to the active
    research area of finite free probability. In contrast to its standard tools, our
    approach allows for non-compactly supported limiting distributions, (barely) complex
    rooted polynomials and even provides the full microscopic description of the roots.
    Moreover, we extend our results to differential operators generating free multiplicative
    infinitely divisible distributions, to the rectangular free convolution, and to
    $f_n(\\partial_z)p_n$ for real rooted polynomials $p_n$, implying a generalization
    of the recent connections between the heat flow and free Brownian motion to any
    free Lévy process.\r\n  As corollaries, we identify free stable distributions
    by choosing $f_n$ to be a fixed rescaled Laguerre--Pólya function, and we prove
    various convergence results on the zero distributions of Jensen polynomials, e.g.
    the limiting root distribution of Jensen polynomial of the Riemann $Ξ$-function
    is given by the Cauchy distribution.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Andrew
      foaf_name: Campbell, Andrew
      foaf_surname: Campbell
  - foaf_Person:
      foaf_givenName: Jonas
      foaf_name: Jalowy, Jonas
      foaf_surname: Jalowy
      foaf_workInfoHomepage: http://www.librecat.org/personId=113768
    orcid: 0000-0001-9624-2685
  dct_date: 2026^xs_gYear
  dct_language: eng
  dct_title: Pólya--Schur problems and free probability@
...