Multideterminantal measures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911056849272832 |
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| author | Kenyon, Richard |
| author_facet | Kenyon, Richard |
| contents | We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, 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 \emph{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 $Gr_{n_1,n}$ having corresponding Plücker coordinates of the same signs.
We also define and completely characterize determinantal probability measures on the permutation group $S_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multideterminantal measures Kenyon, Richard Probability 60C05 We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, 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 \emph{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 $Gr_{n_1,n}$ having corresponding Plücker coordinates of the same signs. We also define and completely characterize determinantal probability measures on the permutation group $S_n$. |
| title | Multideterminantal measures |
| topic | Probability 60C05 |
| url | https://arxiv.org/abs/2501.18349 |