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| Format: | Preprint |
| Published: |
2022
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| Online Access: | https://arxiv.org/abs/2212.11452 |
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| _version_ | 1866910646688284672 |
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| author | Kivimae, Pax |
| author_facet | Kivimae, Pax |
| contents | We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in this model was recently computed by Fyodorov [32] in the high-dimensional limit, followed a similar computation for the expected number of stable equilibria by Garcia [38]. We show that for $p > 9$ the number of equilibria, as well as the number of stable equilibria, concentrate around their respective averages, generalizing recent results of Subag and Zeitouni [61, 64] in the relaxational case. In particular, we confirm that this model undergoes a transition from relative to absolute instability, in the sense of Ben Arous, Fyodorov, and Khoruzhenko [11]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11452 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Concentration of Equilibria and Relative Instability in Disordered Non-Relaxational Dynamics Kivimae, Pax Probability We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in this model was recently computed by Fyodorov [32] in the high-dimensional limit, followed a similar computation for the expected number of stable equilibria by Garcia [38]. We show that for $p > 9$ the number of equilibria, as well as the number of stable equilibria, concentrate around their respective averages, generalizing recent results of Subag and Zeitouni [61, 64] in the relaxational case. In particular, we confirm that this model undergoes a transition from relative to absolute instability, in the sense of Ben Arous, Fyodorov, and Khoruzhenko [11]. |
| title | Concentration of Equilibria and Relative Instability in Disordered Non-Relaxational Dynamics |
| topic | Probability |
| url | https://arxiv.org/abs/2212.11452 |