Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computation of Power Law Equilibrium Measures on Balls of Arbitrary
  Dimension   We present a numerical approach for computing attractive-repulsive power law
equilibrium measures in arbitrary dimension. We prove new recurrence
relationships for radial Jacobi polynomials on $d$-dimensional ball domains,
providing a substantial generalization of the work based on recurrence
relationships of Riesz potentials on arbitrary dimensional balls. Among the
attractive features of the numerical method are good efficiency due to
recursively generated banded and approximately banded Riesz potential operators
and computational complexity independent of the dimension $d$, in stark
contrast to the widely used particle swarm simulation approaches for these
problems which scale catastrophically with the dimension. We present several
numerical experiments to showcase the accuracy and applicability of the method
and discuss how our method compares with alternative numerical approaches and
conjectured analytical solutions which exist for certain special cases.
Finally, we discuss how our method can be used to explore the analytically
poorly understood gap formation boundary to spherical shell support.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga