Abstract: We are aware of many results for the limiting spectral distribution (LSD) of random matrices whose dimension increases indefinitely when certain patterns are assumed for the entries. In this talk we will consider different variations of some of the known random matrices and some new matrices also. Results are obtained for the LSD of these matrices. We start this talk with band matrices. These are the usual patterned matrices, commonly dealt in LDRM literature, with some band structure. We try to obtain the LSD of these band matrices. Next we try to obtain the LSD of sample autocovariance matrices.Studying the LSD of this matrix is important due to its key role in Time Series Analysis. We also move further, to a variation of sample autocovariance matrix and we call it sample autocovariance type matrices. Then we define a new class of matrices called variant matrices and look for its LSD. All the steps except the Carleman condition will be discussed. To wrap up we will define a class of link function $\left\{L_p \,:\, p \in (0, 2] \,\right\}$ where $L_p(i, j) = i+j$ mod $\floor np \rfloor$. Hankel and Reverse Circulant link function are two special choices in this class. We will discuss the results for this and will try to see how LSD varies as p changes.

[This is a joint work with Arup Bose]