README.md

LUE-patterns

Regression on LUE eigenvalues

We implement Anna Maltsev's idea of fitting a linear model (doing linear regression) on the Laguerre Unitary Ensemble (LUE) eigenvalues for a fixed LUE parameter $\alpha = 4$. More details are at the beginning of each notebook.

Some remarks:

• the dataset contains three sets of files, for number of eigenvalues $N=1000, 5000, 10000$. For each $N$, due to Github restrictions on file size, there are 4 files which need to be concatenated. Under Linux or MacOS you can simply run the following three separate commands:

cat LUE_N_1000_alpha_4.00_xa*.txt > LUE_N_1000_alpha_4.00.txt
cat LUE_N_5000_alpha_4.00_xa*.txt > LUE_N_5000_alpha_4.00.txt
cat LUE_N_10000_alpha_4.00_xa*.txt > LUE_N_10000_alpha_4.00.txt

• we use both Julia and Python
• if the only difference between two files is julia vs python in the respective file names, they do the same thing, but in slightly different ways
• there are Markdown files (ending in .md in the notebooks folder) which, when clicked, give a pretty neat webpage of each individual notebook
• this repository is constantly changing/being refined as more tests are being performed