Triplets of local minima in a high-dimensional random landscape: Correlations, clustering, and memoryless activated jumps
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| Format: | Preprint |
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2024
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| _version_ | 1866915190396682240 |
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| author | Pacco, Alessandro Rosso, Alberto Ros, Valentina |
| author_facet | Pacco, Alessandro Rosso, Alberto Ros, Valentina |
| contents | We compute the distribution of triplets of stationary points in the energy landscape of the spherical p-spin model, by evaluating the quenched three-point complexity by means of the Kac-Rice formalism. We show the occurrence of transitions in the organization of stationary points in the landscape, identifying regions where local minima and saddles accumulate and cluster around other stationary points, thus displaying the presence of correlations in the landscape. We discuss the implications of these findings for the dynamical exploration of the energy landscape in the activated regime, specifying conditions under which transitions between local minima are expected to exhibit correlated rates and when, conversely, activated jumps are likely to be memoryless. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triplets of local minima in a high-dimensional random landscape: Correlations, clustering, and memoryless activated jumps Pacco, Alessandro Rosso, Alberto Ros, Valentina Disordered Systems and Neural Networks Statistical Mechanics We compute the distribution of triplets of stationary points in the energy landscape of the spherical p-spin model, by evaluating the quenched three-point complexity by means of the Kac-Rice formalism. We show the occurrence of transitions in the organization of stationary points in the landscape, identifying regions where local minima and saddles accumulate and cluster around other stationary points, thus displaying the presence of correlations in the landscape. We discuss the implications of these findings for the dynamical exploration of the energy landscape in the activated regime, specifying conditions under which transitions between local minima are expected to exhibit correlated rates and when, conversely, activated jumps are likely to be memoryless. |
| title | Triplets of local minima in a high-dimensional random landscape: Correlations, clustering, and memoryless activated jumps |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2410.18010 |