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