diff --git a/_site/atom.xml b/_site/atom.xml index 48c855c..bd82b6c 100644 --- a/_site/atom.xml +++ b/_site/atom.xml @@ -50,18 +50,16 @@

I find this mildly fascinating that such a straightforward definition of a random matrix can exhibit such non-random properties in their spectrum.

Simulation

I ran a quick simulation, thanks to Julia’s great ecosystem for linear algebra and statistical distributions:

-
using Distributions
-using LinearAlgebra
-using UnicodePlots
-
-function ginibre(n)
-d = Normal(0, sqrt(1/2n))
-reshape(rand(d, n^2), (n,n)) + im*reshape(rand(d, n^2), (n,n))
-end
+
+scatterplot(real(v), imag(v), xlim=[-1.5,1.5], ylim=[-1.5,1.5])

I like using UnicodePlots for this kind of quick-and-dirty plots, directly in the terminal. Here is the output:

References

diff --git a/_site/posts/ginibre-ensemble.html b/_site/posts/ginibre-ensemble.html index b3edf1e..187b909 100644 --- a/_site/posts/ginibre-ensemble.html +++ b/_site/posts/ginibre-ensemble.html @@ -38,18 +38,16 @@

I find this mildly fascinating that such a straightforward definition of a random matrix can exhibit such non-random properties in their spectrum.

Simulation

I ran a quick simulation, thanks to Julia’s great ecosystem for linear algebra and statistical distributions:

-
using Distributions
-using LinearAlgebra
-using UnicodePlots
-
-function ginibre(n)
-d = Normal(0, sqrt(1/2n))
-reshape(rand(d, n^2), (n,n)) + im*reshape(rand(d, n^2), (n,n))
-end
+
+scatterplot(real(v), imag(v), xlim=[-1.5,1.5], ylim=[-1.5,1.5])

I like using UnicodePlots for this kind of quick-and-dirty plots, directly in the terminal. Here is the output:

References

diff --git a/_site/rss.xml b/_site/rss.xml index 9d54f11..8b72bbf 100644 --- a/_site/rss.xml +++ b/_site/rss.xml @@ -46,18 +46,16 @@

I find this mildly fascinating that such a straightforward definition of a random matrix can exhibit such non-random properties in their spectrum.

Simulation

I ran a quick simulation, thanks to Julia’s great ecosystem for linear algebra and statistical distributions:

-
using Distributions
-using LinearAlgebra
-using UnicodePlots
-
-function ginibre(n)
-d = Normal(0, sqrt(1/2n))
-reshape(rand(d, n^2), (n,n)) + im*reshape(rand(d, n^2), (n,n))
-end
+
+scatterplot(real(v), imag(v), xlim=[-1.5,1.5], ylim=[-1.5,1.5])

I like using UnicodePlots for this kind of quick-and-dirty plots, directly in the terminal. Here is the output:

References

diff --git a/posts/ginibre-ensemble.org b/posts/ginibre-ensemble.org index 451e23f..f5f993a 100644 --- a/posts/ginibre-ensemble.org +++ b/posts/ginibre-ensemble.org @@ -32,13 +32,11 @@ date: 2019-03-20 algebra and statistical distributions: #+begin_src julia - using Distributions using LinearAlgebra using UnicodePlots function ginibre(n) - d = Normal(0, sqrt(1/2n)) - reshape(rand(d, n^2), (n,n)) + im*reshape(rand(d, n^2), (n,n)) + return randn((n, n)) * sqrt(1/2n) + im * randn((n, n)) * sqrt(1/2n) end v = eigvals(ginibre(2000))