Statistics of the number of minima in a random energy landscape.
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 two- to five-dimensional hypercubic lattices, we compute the exponent numerically and compare to the Cayley tree case.
Majumdar
Satya N
SN
CNRS, Université Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France.
Martin
Olivier C
OC