@unpublished{59210,
  abstract     = {{We establish basic properties of the heat flow on entire holomorphic
functions that have order at most 2. We then look specifically at the action of
the heat flow on the Gaussian analytic function (GAF). We show that applying
the heat flow to a GAF and then rescaling and multiplying by an exponential of
a quadratic function gives another GAF. It follows that the zeros of the GAF
are invariant in distribution under the heat flow, up to a simple rescaling.
  We then show that the zeros of the GAF evolve under the heat flow
approximately along straight lines, with an error whose distribution is
independent of the starting point. Finally, we connect the heat flow on the GAF
to the metaplectic representation of the double cover of the group
$SL(2;\mathbb{R}).$}},
  author       = {{Hall, Brian and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}},
  booktitle    = {{arXiv:2304.06665}},
  title        = {{{The heat flow, GAF, and SL(2;R)}}},
  year         = {{2023}},
}