The limit shape of large alternating sign matrices
Mathematical Physics
2012-03-13 v2 Combinatorics
math.MP
Abstract
The problem of the limit shape of large alternating sign matrices (ASMs) is addressed by studying the emptiness formation probability (EFP) in the domain-wall six-vertex model. Assuming that the limit shape arises in correspondence to the `condensation' of almost all solutions of the saddle-point equations for certain multiple integral representation for EFP, a conjectural expression for the limit shape of large ASMs is derived. The case of 3-enumerated ASMs is also considered.
Cite
@article{arxiv.0803.2697,
title = {The limit shape of large alternating sign matrices},
author = {F. Colomo and A. G. Pronko},
journal= {arXiv preprint arXiv:0803.2697},
year = {2012}
}
Comments
14 pages, 4 figures; v2: presentation expanded, one figure (Fig. 4) added, a variant of the accepted version of the paper, specially made for arXiv