Very persistent random walkers reveal transitions in landscape topology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918364742418432 |
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| author | Kent-Dobias, Jaron |
| author_facet | Kent-Dobias, Jaron |
| contents | We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical glass transition, but persistent walks remain ergodic at lower energies. In models where the energy landscape is thoroughly understood, we show that, in the limit of infinite persistence time, the ergodicity-breaking transition coincides with a transition in the topology of microcanonical configuration space. We conjecture that this correspondence generalizes to other models, and use it to determine the topological transition energy in situations where the landscape properties are ambiguous. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Very persistent random walkers reveal transitions in landscape topology Kent-Dobias, Jaron Disordered Systems and Neural Networks Statistical Mechanics We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical glass transition, but persistent walks remain ergodic at lower energies. In models where the energy landscape is thoroughly understood, we show that, in the limit of infinite persistence time, the ergodicity-breaking transition coincides with a transition in the topology of microcanonical configuration space. We conjecture that this correspondence generalizes to other models, and use it to determine the topological transition energy in situations where the landscape properties are ambiguous. |
| title | Very persistent random walkers reveal transitions in landscape topology |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2505.16653 |