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

共 28 条

[21] CALCULATION OF NORMS OF BETHE WAVE-FUNCTIONS [J].

KOREPIN, VE .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 86 (03) :391-418

[22]

Kuperberg G., 1996, INT MATH RES NOTICES, V1996, P139, DOI [10.1155/S1073792896000128, DOI 10.1155/S1073792896000128]

[23] KAZAKOV-MIGDAL MODEL WITH LOGARITHMIC POTENTIAL AND THE DOUBLE PENNER MATRIX MODEL [J].

PANIAK, L ;

WEISS, N .

JOURNAL OF MATHEMATICAL PHYSICS, 1995, 36 (05) :2512-2530

[24]

PENNER RC, 1988, J DIFFER GEOM, V27, P35

[25]

Propp J., 2001, DISCRETE MATH THEOR, P43

[26]

Syljuåsen OF, 2004, PHYS REV E, V70, DOI 10.1103/PhysRevE.70.016118

[27]

Takhtadzhan L. A., 1979, Russ. Math. Surv., V34, P11

[28]

WIELAND B, 2008, COMMUNICATION 0110

← 1 2 3 →