  Determinantal point processes are point processes whose correlation functions
are given by determinants of matrices. The entries of these matrices are given
by one fixed function of two variables, which is called the kernel of the point
process. It is well-known that there are different kernels that induce the same
correlation functions. We classify all the possible transformations of a kernel
that leave the induced correlation functions invariant, restricting to the case
of symmetric kernels.
