@article{TEXTUAL,
      recid = {11704},
      author = {Boltz, Horst-Holger and Kurchan, Jorge and Liu, Andrea J.},
      title = {Fluctuation distributions of energy minima in complex  landscapes},
      journal = {Physical Review Research},
      address = {2021-01-19},
      number = {TEXTUAL},
      abstract = {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 nontrivial finite-size  scaling. Based on this, we propose a picture of  gradient-descent dynamics that highlights the importance of  a first-passage process in the eigenvalues of the Hessian.  This picture provides a concrete link to problems in which  the Tracy-Widom distribution is established. Aspects of  this first-passage view of gradient-descent dynamics are  generic for nonconvex complex landscapes, rationalizing the  commonality that we find across models.Received 2 December  2019Accepted 18 December  2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013061Published  by the American Physical Society under the terms of the  Creative Commons Attribution 4.0 International license.  Further distribution of this work must maintain attribution  to the author(s) and the published article's title, journal  citation, and DOI.Published by the American Physical  SocietyPhysics Subject Headings (PhySH)Research  AreasBoolean satisfiability problemNP-hard problemsPhysical  SystemsGlassesSpin glassesTechniquesBrownian  dynamicsComputational complexityRandom matrix  theoryStochastic differential equationsStatistical Physics},
      url = {http://knowledge.uchicago.edu/record/11704},
}