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

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

2006-09-28

arxiv.org/abs/cond-mat/0609735v2

Phys. Rev. E 74, 061112 (2006).

Physics

Condensed Matter

Statistical Mechanics

18 pages, 8 figures, added background on landscapes and references

Scientific paper

10.1103/PhysRevE.74.061112

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.

Affiliated with

Also associated with

No associations

Rating

The Statistics of the Number of Minima in a Random Energy Landscape does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Statistics of the Number of Minima in a Random Energy Landscape, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Statistics of the Number of Minima in a Random Energy Landscape will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531561