Reciprocal maximum likelihood degrees of diagonal linear concentration models

11/28/2020

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by   Christopher Eur, et al.

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We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model ℒ⊆ℂ^n of dimension r is equal to (-2)^rχ_M( 1/2), where χ_M 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.