ABSTRACT
We begin the chapter with the notions of empirical and limiting spectral distribution of large random matrices. One of the most useful and common methods to establish the limiting spectral distribution of a sequence of real symmetric matrices is the moment method. There are two circulant-type matrices which are symmetric, namely SCn and RCn . We establish the limiting spectral distribution of these two matrices by the moment method. The limits are universal; that is, they do not depend on the underlying distribution of the entries. The non-symmetric circulants will be tackled in the later chapters.
