Distribution of rare saddles in the p  -spin energy landscape

We compute the statistical distribution of index-1 saddles surrounding a given local minimum of the $p$-spin energy landscape, as a function of their distance to the minimum in configuration space and of the energy of the latter. We identify the saddles also in the region of configuration space in w...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-03, Vol.53 (12), p.125002
Main Author: Ros, Valentina
Format: Article
Language:English
Subjects:
Physics
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Summary:We compute the statistical distribution of index-1 saddles surrounding a given local minimum of the $p$-spin energy landscape, as a function of their distance to the minimum in configuration space and of the energy of the latter. We identify the saddles also in the region of configuration space in which they are subdominant in number (i.e., rare) with respect to local minima, by computing large deviation probabilities of the extremal eigenvalues of their Hessian. As an independent result, we determine the joint large deviation probability of the smallest eigenvalue and eigenvector of a GOE matrix perturbed with both an additive and multiplicative finite-rank perturbation.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab73ac