Reciprocal maximum likelihood degrees of diagonal linear concentration models
Christopher Eur, Tara Fife, José Alejandro Samper, and Tim Seynnaeve
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Submission date: 02. Dec. 2020
Keywords and phrases: maximum likelihood degrees, reciprocal spaces, matroids, characteristic polynomials
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We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model ℒ⊆ ℂn of dimension r is equal to (−2)rχM(), 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.