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Computational Random Matrix Theory

By Robert Sweeney Blanco

This is an expository textbook for the field of Random Matrix Theory. In addition to providing established theoretical results, we will simulate results using Python 3 to provide emperical intuition. All code written for this textbook is provided in coding cells like the one shown below.

1+1

2

For the sake of compactness, some coding cells are in hidden cells. To preview hidden cells, click the gray plus sign. An example of a hidden cell is below.

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

%matplotlib inline
sns.set()

x = np.linspace(-2, 2, 100)
y = x**2
plt.xlabel("x")
plt.ylabel("$x^2$")
plt.plot(x,y);

The Python library RandomMatrix was written for this textbook and will be demonstrated throughout the text. The code can be found in this repository.

Special thanks to Jorge Garza Vargas for invaluable contributions to the text and Nikhil Srivastava for his sponsorship.