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Résumé |
Understanding the statistical properties of the stationary points of high-dimensional, random energy landscapes is a central problem in the physics of glassy systems, as well as in interdisciplinary applications to computer science, ecology and biology. In this talk, I will discuss a framework to perform the computation of the quenched complexity of stationary points, making use of a replicated version of the Kac-Rice formula. I will discuss its application to simple models (the spiked tensor model and its generalizations) which capture the competition between a deterministic signal and stochastic noise, and correspond to a spherical p-spin Hamiltonian endowed with ferromagnetic multi-body interaction terms. I will describe the phase transitions that occur in the structure of the landscape when changing the signal-to-noise ratio, and highlight the implications for the evolution of local dynamics within the landscape.
Reference:
Valentina Ros, Gerard Ben Arous, Giulio Biroli and Chiara Cammarota, Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions, preprint cond-mat arXiv:1804.02686
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