Multideterminantal measures

2025/01/30 by Richard Kenyon, Kenyon, Richard
Mathematics · #60C05 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2501.18349

openalex publication_date 2025/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define multideterminantal probability measures, a family of probability measures on [k]ⁿ where [k]=\1,2,…,k\, generalizing determinantal measures (which correspond to the case k=2). We give examples coming from the positive Grassmannian, from the dimer model and from the spanning tree model. We characterize kernels of pure k-determinantal measures as those arising from k-tuples of Grassmannian elements whose maximal minors have certain sign restrictions. As a special case we construct all kernels of pure determinantal measures via a pair of elements of Gr_n1,n having corresponding Plücker coordinates of the same signs. We also define and completely characterize determinantal probability measures on the permutation group S_n.

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