Phase transitions from $\exp (n^{1/2})$ to $\exp (n^{2/3})$ in the asymptotics of banded plane partitions

Abstract

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 $c_1,\dots ,c_5$. 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.

32 pages, 4 figures, submitted

References in corpus (1)

• Skew doubled shifted plane partitions: calculus and asymptotics