THE LIMIT SHAPE OF LARGE ALTERNATING SIGN MATRICES

被引：31

作者：

Colomo, F. ^{[1
]}

Pronko, A. G. ^{[2
]}

机构：

[1] Ist Nazl Fis Nucl, Sez Firenze, I-50019 Sesto Fiorentino, FI, Italy

[2] Russian Acad Sci, St Petersburg Dept, VA Steklov Math Inst, St Petersburg 191023, Russia

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2010年 / 24卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

six-vertex model; domain wall boundary conditions; alternating sign matrices; asymptotic limit shapes; phase separation phenomena; random matrix models; emptiness formation probability; condensation hypothesis; WALL BOUNDARY-CONDITIONS; 6-VERTEX MODEL;

D O I：

10.1137/080730639

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 with the "condensation" of almost all solutions of the saddle-point equations for certain multiple integral representations for EFP, a conjectural expression for the limit shape of large ASMs is derived. The case of 3-enumerated ASMs is also considered.

引用

页码：1558 / 1571

页数：14

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