---
res:
  bibo_abstract:
  - 'We study the evolution of zeros of high polynomial powers under the heat flow.
    For any fixed polynomial $P(z)$, we prove that the empirical zero distribution
    of its heat-evolved $n$-th power converges to a distribution on the complex plane
    as $n$ tends to infinity. We describe this limit distribution $μ_t$ as a function
    of the time parameter $t$ of the heat evolution: For small time, zeros start to
    spread out in approximately semicircular distributions, then intricate curves
    start to form and merge, until for large time, the zero distribution approaches
    a widespread semicircle law through the initial center of mass. The Stieltjes
    transform of the limit distribution $μ_t$ satisfies a self-consistent equation
    and a Burgers'' equation. The present paper deals with general complex-rooted
    polynomials for which, in contrast to the real-rooted case, no free-probabilistic
    representation for $μ_t$ is available.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Antonia
      foaf_name: Höfert, Antonia
      foaf_surname: Höfert
      foaf_workInfoHomepage: http://www.librecat.org/personId=115802
  - foaf_Person:
      foaf_givenName: Jonas
      foaf_name: Jalowy, Jonas
      foaf_surname: Jalowy
  - foaf_Person:
      foaf_givenName: Zakhar
      foaf_name: Kabluchko, Zakhar
      foaf_surname: Kabluchko
  dct_date: 2025^xs_gYear
  dct_language: eng
  dct_title: Zeros of polynomial powers under the heat flow@
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