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The Statistics of the Number of Minima in a Random Energy Landscape

Satya N. Majumdar·Olivier C. Martin
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Abstract

We consider random energy landscapes constructed from d-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large deviation principle and we derive the associated law exactly for dimension 1. Also of interest is the probability of the maximum possible number of minima; this probability scales exponentially with the number of sites. We calculate analytically the corresponding exponent for the Cayley tree and the two-leg ladder; for 2 to 5 dimensional hypercubic lattices, we compute the exponent numerically and compare to the Cayley tree case.

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Satya N. Majumdar, Olivier C. Martin. 2006-11-20. The Statistics of the Number of Minima in a Random Energy Landscape. https://doi.org/10.1103/physreve.74.061112

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