Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of random polynomials with independent roots   We consider the zeros of the sum of independent random polynomials as their
degrees tend to infinity. Namely, let $p$ and $q$ be two independent random
polynomials of degree $n$, whose roots are chosen independently from the
probability measures $\mu$ and $\nu$ in the complex plane, respectively. We
compute the limiting distribution for the zeros of the sum $p+q$ as $n$ tends
to infinity. The limiting distribution can be described by its logarithmic
potential, which we show is the pointwise maximum of the logarithmic potentials
of $\mu$ and $\nu$. More generally, we consider the sum of $m$ independent
degree $n$ random polynomials when $m$ is fixed and $n$ tends to infinity. Our
results can be viewed as describing a version of the free additive convolution
from free probability theory for zeros of polynomials.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics