Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limiting empirical distribution of zeros and critical points of random
  polynomials agree in general   In this article, we study critical points (zeros of derivative) of random
polynomials. Take two deterministic sequences $\{a_n\}_{n\geq1}$ and
$\{b_n\}_{n\geq1}$ of complex numbers whose limiting empirical measures are
same. By choosing $\xi_n = a_n$ or $b_n$ with equal probability, define the
sequence of polynomials by $P_n(z)=(z-\xi_1)\dots(z-\xi_n)$. We show that the
limiting measure of zeros and critical points agree for this sequence of random
polynomials under some assumption. We also prove a similar result for
triangular array of numbers. A similar result for zeros of generalized
derivative (can be thought as random rational function) is also proved.
Pemantle and Rivin initiated the study of critical points of random
polynomials. Kabluchko proved the result considering the zeros to be i.i.d.
random variables.

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The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: physics
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph