English

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.

Keywords

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

R2 v1 2026-06-21T10:22:33.937Z