ABSTRACT
In Chapter 1, we have derived explicit formulae for the eigenvalues of circulant-type matrices. This makes the method of normal approximation ideally suited for studying their LSD. In this chapter we show how normal approximation can be used to establish the LSD of circulant-type random matrices, symmetric as well as non-symmetric, with independent entries. The case of dependent entries will be treated in the next chapter. In the later chapters, more sophisticated normal approximation results will be used to study extreme eigenvalues and spectral gaps.
