English

Stick-Breaking Model for Variable-Range Hopping

Disordered Systems and Neural Networks 2009-11-13 v1

Abstract

We consider the optimal conduction path of the one-dimensional variable-range hopping problem. We describe a hierarchical procedure for constructing the path which is in excellent agreement with numerical results obtained from a percolation approach. The advantage of the hierarchical construction is that it is easier to analyse. We show that the distribution of hopping lengths is well approximated by a model for the repeated breaking of a stick at its weakest point, until the fragments are too strong to be broken.

Keywords

Cite

@article{arxiv.0709.3317,
  title  = {Stick-Breaking Model for Variable-Range Hopping},
  author = {M. Wilkinson and B. Mehlig and V. Bezuglyy},
  journal= {arXiv preprint arXiv:0709.3317},
  year   = {2009}
}

Comments

4 pages, 3 figures

R2 v1 2026-06-21T09:19:46.453Z