Calculate equilibrium measures from potentials
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
- Zeros of orthogonal polynomials
- Fekete (near optimal interpolation) points
- 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")