2007 年 61 巻 1 号 p. 169-189
We give a probabilistic expression of the α-determinant by using the Wishart distribution on the cone of positive definite matrices. As a corollary, we give a partial answer to a positivity problem for the α-determinant which is equivalent to the existence problem of certain multivariate probability distributions. We also give a concrete example to support our conjecture for the positivity.