TracyWidom

This is a Julia implementation of Bornemann's method of evaluating the Fredholm determinant associated with the Tracy-Widom distribution.

Provides TWcdf giving the Tracy-Widom CDFs for Dyson index 1, 2, or 4. The keyword argument num_points specifies the number of points in the Gauss-Legendre quadrature, with a default of 25.

Sample usage

using TracyWidom
TWcdf(0,beta=1)
0.8319080662029523
TWcdf(0,beta=2)
0.9693728283552623
TWcdf([0.1,0.2],beta=1)
2-element Array{Float64,1}:
 0.849358
 0.865444

References

• Folkmar Bornemann "On the numerical evaluation of Fredholm determinants", Mathematics of Computation, Volume 79, Number 270, April 2010, Pages 871–915 [pdf] [doi]