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Complexity and accessibility of random landscapes

Sakshi Pahujani, Joachim Krug

SciPost Phys. Lect. Notes 108 (2025) · published 22 December 2025

Part of the 2024-07: Theory of Large Deviations and Applications Collection in the Les Houches Summer School Lecture Notes Series.

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.


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