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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.22120 |
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| _version_ | 1866910109864558592 |
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| author | Kosmakov, Maksim |
| author_facet | Kosmakov, Maksim |
| contents | We construct a unitarily invariant Hermitian matrix ensemble whose fixed-time eigenvalue law coincides with the Karlin--McGregor law for non-intersecting Brownian bridges with arbitrary finite multiplicities at both endpoints. This provides an explicit matrix-ensemble realization of the known mixed-type multiple orthogonal polynomial and Riemann--Hilbert description of the general multi-start/multi-end problem. We then derive several exact finite-$n$ consequences of this construction. These include a path-space lift as an orbital Hermitian Brownian bridge and a reduction of the partition function to a single compact HCIZ integral with explicit $t$-dependence. We also compare the one-sided reduction with the Gaussian external-field ensemble, showing that, although the two ensembles are spectrally equivalent, their angular statistics are different. Finally, we derive fixed-time Schwinger--Dyson identities and associated resolvent relations for the dressed ensemble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Two-HCIZ Gaussian Matrix Model for Non-intersecting Brownian Bridges Kosmakov, Maksim Mathematical Physics High Energy Physics - Theory Probability We construct a unitarily invariant Hermitian matrix ensemble whose fixed-time eigenvalue law coincides with the Karlin--McGregor law for non-intersecting Brownian bridges with arbitrary finite multiplicities at both endpoints. This provides an explicit matrix-ensemble realization of the known mixed-type multiple orthogonal polynomial and Riemann--Hilbert description of the general multi-start/multi-end problem. We then derive several exact finite-$n$ consequences of this construction. These include a path-space lift as an orbital Hermitian Brownian bridge and a reduction of the partition function to a single compact HCIZ integral with explicit $t$-dependence. We also compare the one-sided reduction with the Gaussian external-field ensemble, showing that, although the two ensembles are spectrally equivalent, their angular statistics are different. Finally, we derive fixed-time Schwinger--Dyson identities and associated resolvent relations for the dressed ensemble. |
| title | A Two-HCIZ Gaussian Matrix Model for Non-intersecting Brownian Bridges |
| topic | Mathematical Physics High Energy Physics - Theory Probability |
| url | https://arxiv.org/abs/2510.22120 |