This talk investigates the asymptotic behavior of the least singular value of a heavy-tailed random matrix model, random matrices with alpha-stable entries. We establish that the asymptotic distribution is the same as in the models with finite variance, for example when the entries of the matrix are Gaussian random variables, as the dimension of the matrices grows to infinity. The methods used to establish the result are based on the three step strategy, an important strategy developed in the last decade in the random matrix theory literature.