ABSTRACT

This chapter is devoted to extending the results of the previous chapter to the k-circulant when n = kg + 1. The main result says that the centered and the scaled spectral radius converges to the Gumbel distribution. To establish this result, we make some intricate study of the eigenvalues of the matrix. We also need an auxiliary result which exhibits the tail behavior of the n-fold product of i.i.d. standard exponential variables. Finally, we also need truncation and normal approximation similar to the ones we used in the previous chapter.