• DOI:10.1016/j.jcta.2014.12.002
Corpus ID: 17290535

Chip-firing and energy minimization on M-matrices

@article{Guzmn2015ChipfiringAE,
  title={Chip-firing and energy minimization on M-matrices},
  author={J. Guzm{\'a}n and Caroline J. Klivans},
  journal={J. Comb. Theory, Ser. A},
  year={2015},
  volume={132},
  pages={14-31}
}

J. Guzmán, Caroline J. Klivans

Published 2015

Computer Science, Mathematics

J. Comb. Theory, Ser. A

We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on the work of Baker and Shokrieh, we extend the concept of energy minimizing chip configurations. Given an M-matrix, we show that there exists a unique energy minimizing configuration in each equivalence class defined by the matrix.We consider the class of z-superstable configurations. We prove that for any M-matrix… CONTINUE READING

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed