Reciprocal maximum likelihood degrees of diagonal linear concentration models

  • C. Eur Stanford University, California, USA
  • T. Fife MPI for Mathematics in the Sciences, Germany
  • J. A. Samper Pontificia Universidad Católica de Chile, Chile
  • T. Seynnaeve University of Bern, Germany


We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model LCn of dimension r is equal to (-2)rχM(1/2), where χM is the characteristic polynomial of the matroid M associated to L. In particular, this establishes the polynomiality of the rmld for general diagonal linear concentration models, positively answering a question of Sturmfels, Timme, and Zwiernik.