具有任意斜率后墙的随机斜平面分拆的标度极限
数学物理
2011-10-21 v2 组合数学
math.MP
概率论
摘要
本文研究了限制在盒子中的随机斜平面分拆的标度极限，其中内形状一致收敛于一个分段线性函数V，其斜率在[-1,1]内任意。结果表明，体中的关联核由不完全Beta核给出，这与预期一致。由此可以确定，标度极限中的局部关联函数不依赖于收敛到V的特定离散内形状序列。本文还详细分析了极限形状顶部和冻结边界处的关联核。结果表明，根据后墙线性段的斜率，系统表现出[OR2]或[BMRT]中观察到的行为。
引用
@article{arxiv.1001.4303,
title = {Scaling limits of random skew plane partitions with arbitrarily sloped back walls},
author = {Sevak Mkrtchyan},
journal= {arXiv preprint arXiv:1001.4303},
year = {2011}
}
备注
29 pages. Version 2: Several sections and proofs were improved and completely rewritten. These include Sections 2.2.2,2.2.4 and 2.2.5, Lemmas 2.3 and 4.2, and Proposition 4.1. Section 1.1.3 was added. This version is to be published in Comm. Math. Phys