有偏平面剖分的平衡收敛性
Convergence to equilibrium of biased plane partitions
摘要：
研究了由平面盒剖分得到的（2+1）维单调曲面的单翻转动力学。该表面被分析为一个系统的不相交的简单路径。当翻转有非零偏置时，我们证明了在边界条件和系统大小中一致存在正的谱隙。在同样的假设下，对于一个系统的大小为M，混合时间被证明是M阶对数校正。
英文摘要：
We study a single-flip dynamics for the monotone surface in (2+1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non-intersecting simple paths. When the flips have a non-zero bias we prove that there is a positive spectral gap uniformly in the boundary conditions and in the size of the system. Under the same assumptions, for a system of size M, the mixing time is shown to be of order M up to logarithmic corrections.
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