Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Root Statistics of Random Polynomials with Bounded Mahler Measure   The Mahler measure of a polynomial is a measure of complexity formed by
taking the modulus of the leading coefficient times the modulus of the product
of its roots outside the unit circle. The roots of a real degree $N$ polynomial
chosen uniformly from the set of polynomials of Mahler measure at most 1 yields
a Pfaffian point process on the complex plane. When $N$ is large, with
probability tending to 1, the roots tend to the unit circle, and we investigate
the asymptotics of the scaled kernel in a neighborhood of a point on the unit
circle. When this point is away from the real axis (on which there is a
positive probability of finding a root) the scaled process degenerates to a
determinantal point process with the same local statistics (i.e., scalar
kernel) as the limiting process formed from the roots of complex polynomials
chosen uniformly from the set of polynomials of Mahler measure at most 1. Three
new matrix kernels appear in a neighborhood of $\pm 1$ which encode information
about the correlations between real roots, between complex roots and between
real and complex roots. Away from the unit circle, the kernels converge to new
limiting kernels, which imply among other things that the expected number of
roots in any open subset of $\C$ disjoint from the unit circle converges to a
positive number. We also give ensembles with identical statistics drawn from
two-dimensional electrostatics with potential theoretic weights, and normal
matrices chosen with regard to their topological entropy as actions on
Euclidean space.

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The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg