The high-d landscapes paradigm: spin-glasses, and beyond

2022/09/16 by Valentina Ros, Ros, Valentina, Yan V. Fyodorov +1 · 1 citation
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2209.07975

Abstract

We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its stationary points and stressing connections with the statistical physics of disordered systems and with random matrix theory.

Cited by

• Overlaps between eigenvectors of spiked, correlated random matrices: from matrix PCA to random Gaussian landscapes

Related

• Exploring high-dimensional random landscapes: from spin glasses to random matrices, passing through simple chaotic systems
• High-dimensional random landscapes: from typical to large deviations
• Counting Vacua in Random Landscapes
• Counting Stationary Points of Random Landscapes as a Random Matrix Problem
• Complexity and accessibility of random landscapes