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Characterizing matrix-exponential distributions of order 4 (abstract only)

The Laplace-Stieltjes transform of a matrix-exponential distribution is a rational function. If there are no common factors between the numerator and denominator polynomials, then the order of the matrix-exponential distribution is the degree of the denominator polynomial. Given a rational Laplace-Stieltjes transform, it is unknown, in general, when it corresponds to a matrix-exponential distribution. Matrix-exponential distributions of order 3 have been completely characterized in this manner, but in this talk we look at the problem of characterizing matrix-exponential distributions of order 4.