Proof of the local REM conjecture for number partitioning II: growing energy scales

Details Proof of the local REM conjecture for number partitioning II: growing energy scales Proof of the local REM conjecture for number partitioning II: growing energy scales

2005-08-25

arxiv.org/abs/cond-mat/0508600v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

42 pages

Scientific paper

We continue our analysis of the number partitioning problem with $n$ weights chosen i.i.d. from some fixed probability distribution with density $\rho$. In Part I of this work, we established the so-called local REM conjecture of Bauke, Franz and Mertens. Namely, we showed that, as $n \to \infty$, the suitably rescaled energy spectrum above some {\it fixed} scale $\alpha$ tends to a Poisson process with density one, and the partitions corresponding to these energies become asymptotically uncorrelated. In this part, we analyze the number partitioning problem for energy scales $\alpha_n$ that grow with $n$, and show that the local REM conjecture holds as long as $n^{-1/4}\alpha_n \to 0$, and fails if $\alpha_n$ grows like $\kappa n^{1/4}$ with $\kappa>0$. We also consider the SK-spin glass model, and show that it has an analogous threshold: the local REM conjecture holds for energies of order $o(n)$, and fails if the energies grow like $\kappa n$ with $\kappa >0$.

Affiliated with

Also associated with

No associations

Rating

Proof of the local REM conjecture for number partitioning II: growing energy scales 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 Proof of the local REM conjecture for number partitioning II: growing energy scales, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proof of the local REM conjecture for number partitioning II: growing energy scales will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-262845