Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913188499423232 |
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| author | Yu, Tingzhou |
| author_facet | Yu, Tingzhou |
| contents | We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into the asymptotic energy limit. Our approach involves integro-differential equations, incorporating the Crisanti-Horner-Sommers-Cugliandolo-Kurchan equation from spin glass literature, to analyze the system's size and its temperature-dependent phase transition. Additionally, we conduct an average case complexity analysis, establishing hitting time bounds for the bottom eigenvector of a Wigner matrix. Our investigation also includes the power iteration algorithm, examining its average case complexity in identifying the top eigenvector overlap, with comprehensive complexity bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors Yu, Tingzhou Probability Numerical Analysis Mathematical Physics We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into the asymptotic energy limit. Our approach involves integro-differential equations, incorporating the Crisanti-Horner-Sommers-Cugliandolo-Kurchan equation from spin glass literature, to analyze the system's size and its temperature-dependent phase transition. Additionally, we conduct an average case complexity analysis, establishing hitting time bounds for the bottom eigenvector of a Wigner matrix. Our investigation also includes the power iteration algorithm, examining its average case complexity in identifying the top eigenvector overlap, with comprehensive complexity bounds. |
| title | Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors |
| topic | Probability Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2401.03668 |