Lanczos Meets Orthogonal Polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917358899036160 |
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| author | Qu, Le-Chen |
| author_facet | Qu, Le-Chen |
| contents | We establish a direct correspondence between the Lanczos approach and the orthogonal polynomials approach in random matrix theory. In the large-$N$ and continuum limits, the average Lanczos coefficients and the recursion coefficients become equivalent, with the precise mapping $b(1-x)=\sqrt{R(x)}$ and $a(1-x)=S(x)$. As a result, the two formalisms yield identical expressions for the leading density of states. We further analyze the Krylov dynamics associated with the recursion coefficients and show that the orthogonal polynomials admit a natural interpretation as Krylov polynomials. This picture is realized explicitly in the Gaussian Unitary Ensemble, where all quantities can be computed analytically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lanczos Meets Orthogonal Polynomials Qu, Le-Chen High Energy Physics - Theory Quantum Physics We establish a direct correspondence between the Lanczos approach and the orthogonal polynomials approach in random matrix theory. In the large-$N$ and continuum limits, the average Lanczos coefficients and the recursion coefficients become equivalent, with the precise mapping $b(1-x)=\sqrt{R(x)}$ and $a(1-x)=S(x)$. As a result, the two formalisms yield identical expressions for the leading density of states. We further analyze the Krylov dynamics associated with the recursion coefficients and show that the orthogonal polynomials admit a natural interpretation as Krylov polynomials. This picture is realized explicitly in the Gaussian Unitary Ensemble, where all quantities can be computed analytically. |
| title | Lanczos Meets Orthogonal Polynomials |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2512.15857 |