Scaling limits of random skew plane partitions with arbitrarily sloped back walls

TL;DR

This paper investigates the scaling limits of random skew plane partitions with arbitrary sloped back walls, revealing universal correlation kernels and detailed boundary behaviors in the limit shape.

Contribution

It establishes the universality of the incomplete Beta kernel in the bulk and analyzes boundary phenomena for skew plane partitions with arbitrary slopes.

Findings

Correlation kernels in the bulk are given by the incomplete Beta kernel.

Local correlation functions are independent of the specific sequence of inner shapes.

Behavior at the top and frozen boundary depends on the slope of the back wall.

Abstract

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk are given by the incomplete Beta kernel, as expected. As a consequence it is established that the local correlation functions in the scaling limit do not depend on the particular sequence of discrete inner shapes that converge to V. A detailed analysis of the correlation kernels at the top of the limit shape and of the frozen boundary is given. It is shown that depending on the slope of the linear section of the back wall, the system exhibits behavior observed in either [OR2] or [BMRT].