Dario Giandinoto: Spectral asymptotics of tridiagonal KMS matrices

KMS matrices are matrices whose entries on the diagonals are obtained by sampling continuous functions on a partition of \([0,1]\). They can be seen as a generalization of Toeplitz matrices, whose entries on the diagonals are constant. In this talk, we will provide numerical computations of the spectrum of KMS matrices, showing how it appears to accumulate on certain curves, similarly to Toeplitz matrices. We will then compute the spectral asymptotics in the case where the diagonals are sampled from piecewise constant functions, and explain how this could be used to study the spectrum of a randomized version of KMS matrices.