### Data dimension, p is fixed but n goes to infinity ######

n<-1000
p<-4
X<-matrix(rnorm(n*p,0,1),n,p)
Sn<-t(X)%*%X/n
eigenvals<-eigen(Sn)$values

n1<-2000
p1<-4
X1<-matrix(rnorm(n1*p1,0,1),n1,p1)
Sn1<-t(X1)%*%X1/n1
eigenvals1<-eigen(Sn1)$values

### Data dimension, p is growing with the sample size n ####

n<-1000
p<-400
X<-matrix(rnorm(n*p,0,1),n,p)
Sn<-t(X)%*%X/n
eigenvals<-eigen(Sn)$values
hist(eigenvals,freq=FALSE)
gamma<-p/n
a<-(1-sqrt(gamma))^2
b<-(1+sqrt(gamma))^2
xvec<-seq(a,b,length=100)
MPrho<-sqrt((b-xvec)*(xvec-a))/(2*pi*gamma*xvec)
lines(xvec,MPrho)

n<-2500
p<-1000
X<-matrix(rnorm(n*p,0,1),n,p)
Sn<-t(X)%*%X/n
eigenvals<-eigen(Sn)$values
hist(eigenvals,freq=FALSE)
gamma<-p/n
a<-(1-sqrt(gamma))^2
b<-(1+sqrt(gamma))^2
xvec<-seq(a,b,length=100)
MPrho<-sqrt((b-xvec)*(xvec-a))/(2*pi*gamma*xvec)
lines(xvec,MPrho)