论文标题
从$ \ exp（n^{1/2}）$过渡到$ \ exp（n^{2/3}）$在带平面分区的渐近学中
Phase transitions from $\exp(n^{1/2})$ to $\exp(n^{2/3})$ in the asymptotics of banded plane partitions
论文作者
论文摘要
We examine the asymptotics of a class of banded plane partitions under a varying bandwidth parameter $m$, and clarify the transitional behavior for large size $n$ and increasing $m=m(n)$ to be from $c_1 n^{-1} \exp(c_2 n^{1/2})$ to $c_3 n^{-49/72} \exp(c_4 N^{2/3} + C_5 N^{1/3}）$对于某些显式系数$ C_1，\ ldots，C_5 $。证明方法是所有阶段的统一鞍点分析，是一般的，可以扩展到其他类别的平面分区。
We examine the asymptotics of a class of banded plane partitions under a varying bandwidth parameter $m$, and clarify the transitional behavior for large size $n$ and increasing $m=m(n)$ to be from $c_1 n^{-1} \exp(c_2 n^{1/2})$ to $c_3 n^{-49/72} \exp(c_4 n^{2/3} + c_5 n^{1/3})$ for some explicit coefficients $c_1, \ldots, c_5$. The method of proof, which is a unified saddle-point analysis for all phases, is general and can be extended to other classes of plane partitions.
