Fluctuation Distributions of Energy Minima in Complex Landscapes

Understand

We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes.

• We find strikingly similar phenomenology across several prototypical models.
• We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin glass model.
• We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and non-trivial finite-size scaling.