The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices

de Jong, Jins; Wulkenhaar, Raimar

Abstract

The asymptotic volume of the polytope of symmetric stochastic matrices can be determined by asymptotic enumeration techniques as in the case of the Birkhoff polytope. These methods can be extended to polytopes of symmetric stochastic matrices with given diagonal, if this diagonal varies not too wildly. To this end, the asymptotic number of symmetric matrices with natural entries, zero diagonal and varying row sums is determined and a third order correction factor to this is examined.