Random Young diagrams and Jacobi Unitary Ensemble
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909889378385920 |
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| author | Nazarov, Anton Sushkov, Matvey |
| author_facet | Nazarov, Anton Sushkov, Matvey |
| contents | We consider random Young diagrams with respect to the measure induced by the decomposition of the $p$-th exterior power of $\mathbb{C}^{n}\otimes \mathbb{C}^{k}$ into irreducible representations of $GL_{n}\times GL_{k}$. We demonstrate that transition probabilities for these diagrams in the limit $n,k,p\to\infty$ with $p\sim nk$ converge to the large $N$ limiting law for the eigenvalues of random matrices in Jacobi Unitary Ensemble. We compute the characters of Young--Jucys--Murphy elements in $\bigwedge^{p}(\mathbb{C}^{n}\otimes\mathbb{C}^{k})$ and discuss their relation to surface counting. We formulate several conjectures on the connection between the correlators in both random ensembles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random Young diagrams and Jacobi Unitary Ensemble Nazarov, Anton Sushkov, Matvey Probability Mathematical Physics Representation Theory 60C05, 15A52 We consider random Young diagrams with respect to the measure induced by the decomposition of the $p$-th exterior power of $\mathbb{C}^{n}\otimes \mathbb{C}^{k}$ into irreducible representations of $GL_{n}\times GL_{k}$. We demonstrate that transition probabilities for these diagrams in the limit $n,k,p\to\infty$ with $p\sim nk$ converge to the large $N$ limiting law for the eigenvalues of random matrices in Jacobi Unitary Ensemble. We compute the characters of Young--Jucys--Murphy elements in $\bigwedge^{p}(\mathbb{C}^{n}\otimes\mathbb{C}^{k})$ and discuss their relation to surface counting. We formulate several conjectures on the connection between the correlators in both random ensembles. |
| title | Random Young diagrams and Jacobi Unitary Ensemble |
| topic | Probability Mathematical Physics Representation Theory 60C05, 15A52 |
| url | https://arxiv.org/abs/2511.03881 |