We study the limiting spectral distribution for a class of circulant type random matrices with heavy tailed input sequence. Unlike the light tailed case where the limit is nonrandom, here the limit is a random probability distribution. We provide an explicit representation of the limit.

The limiting spectral distribution of random matrices is known only in a few special situations. In this article, we derive the limiting spectral distribution of a particular variant of a circulant random matrix. Our simulations demonstrate that the convergence to the limit is quite fast. Our...