The limit shape of large alternating sign matrices

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.

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

References in corpus (2)

• The arctic curve of the domain-wall six-vertex model
• Emptiness formation probability in the domain-wall six-vertex model

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