The limit shape of large alternating sign matrices

Details The limit shape of large alternating sign matrices The limit shape of large alternating sign matrices

2008-03-18

arxiv.org/abs/0803.2697v2

SIAM J. Discrete Math. 24 (2010), 1558-1571

Physics

Mathematical Physics

14 pages, 4 figures; v2: presentation expanded, one figure (Fig. 4) added, a variant of the accepted version of the paper, spe

Scientific paper

10.1137/080730639

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.

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