File Exchange

## Marchenko Pastur Law

version 1.0.0.0 (1.67 KB) by Youssef Khmou

### Youssef Khmou (view profile)

Simulation In random Matrix Theory

Updated 30 Jan 2015

In Random Matrix Theory, MP law gives the probability density function of singular values of large rectangular random matrices; when the dimensions of matrix tend to infinity.
This contribution illustrates the PDF of matrix Y(N,N)=(T^-1)X*X^T, where X is random matrix whose entries X_i,j are independent and identically distributed random variables with zero mean and variance s^2. The program is applicable for both uniform and random distributions.
Ref :
Marchenko,V. A., Pastur, L. A. (1967) "Distribution of eigenvalues for some sets of
random matrices", Mat. Sb. (N.S.), 72(114):4, 507–536

### Cite As

Youssef Khmou (2020). Marchenko Pastur Law (https://www.mathworks.com/matlabcentral/fileexchange/49438-marchenko-pastur-law), MATLAB Central File Exchange. Retrieved .

Brent Foster

Thuong Nguyen

cthywu

### cthywu (view profile)

In the example, N=400; T=700, c=N/T < 1, i.e., N<T.
What if N>T?

Santiago Fortes

### Santiago Fortes (view profile)

Thanks for the code.

Prasanta Saikia

### Prasanta Saikia (view profile)

For the normalization of the eigenvalue distribution, you are writing "f=f/sum(f)". But I think this is incorrect; it should be "f=f/trapz(lambda,f)". That is, it should be divided by the area of the histograms. You can refer to this link for the explanation: http://stackoverflow.com/questions/5320677/how-to-normalize-a-histogram-in-matlab

##### MATLAB Release Compatibility
Created with R2007a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux