https://github.com/juliaapproximation/equilibriummeasures.jl

Calculate equilibrium measures from potentials
https://github.com/juliaapproximation/equilibriummeasures.jl

Last synced: 4 months ago
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Calculate equilibrium measures from potentials

• Host: GitHub
• URL: https://github.com/juliaapproximation/equilibriummeasures.jl
• Owner: JuliaApproximation
• License: mit
• Created: 2015-07-24T07:42:34.000Z (almost 11 years ago)
• Default Branch: master
• Last Pushed: 2025-02-13T00:55:50.000Z (over 1 year ago)
• Last Synced: 2025-02-20T21:41:19.690Z (over 1 year ago)
• Language: Julia
• Size: 128 KB
• Stars: 2
• Watchers: 8
• Forks: 1
• Open Issues: 22
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# EquilbriumMeasures

Calculate equilibrium measures from potentials

[![Build Status](https://github.com/JuliaApproximation/EquilibriumMeasures.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/EquilibriumMeasures.jl/actions)

[![codecov](https://codecov.io/gh/JuliaApproximation/EquilibriumMeasures.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/EquilibriumMeasures.jl)

[![DOI](https://zenodo.org/badge/39618532.svg)](https://zenodo.org/badge/latestdoi/39618532)

In potential theory, the equilibrium measure is the limiting distribution of charges in a potential field that minimises energy, see [Saff and Totic 1997](https://www.springer.com/gp/book/9783540570783) and [Deift 1999](https://bookstore.ams.org/cln-3). 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](https://github.com/dlfivefifty/RHPackage).

```julia

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")

```