Calculate equilibrium measures from potentials

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In potential theory, the equilibrium measure is the limiting distribution of charges in a potential field that minimises energy, see Saff and Totic 1997 and Deift 1999. These distributions also describe the distribution of

  1. Zeros of orthogonal polynomials
  2. Fekete (near optimal interpolation) points
  3. Eigenvalues of random matrices This package facilitates their computation, and is based on RHPackage.
using EquilibriumMeasures, Plots
plot(equilibriummeasure(x -> x^2); label="Semicircle", legend=:topleft)
plot!(equilibriummeasure(x -> x^4); label="x^4")
plot!(equilibriummeasure(x -> x^100); label="x^100")
plot!(equilibriummeasure(x -> exp(x) - x); label="exp(x) - x")