English

Complexity and accessibility of random landscapes

Populations and Evolution 2025-12-24 v2 Disordered Systems and Neural Networks Probability

Abstract

These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer science are mentioned where appropriate. Elementary and advanced results on the structure of landscapes are described with a focus on features that are relevant to evolutionary searches, such as the number of local maxima and the existence of fitness-monotonic paths. The recent discovery of submodularity as a biologically meaningful property of fitness landscapes and its consequences for their accessibility is discussed in detail.

Keywords

Cite

@article{arxiv.2502.05896,
  title  = {Complexity and accessibility of random landscapes},
  author = {Sakshi Pahujani and Joachim Krug},
  journal= {arXiv preprint arXiv:2502.05896},
  year   = {2025}
}

Comments

Lecture notes for the Les Houches summer school "Theory of Large Deviations and Applications"; 22 pages, 7 figures. The discussion of basins of attraction has been expanded and additional references have been added

R2 v1 2026-06-28T21:37:44.771Z