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

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

2010-01-25

arxiv.org/abs/1001.4303v2

Comm. Math. Phys. 305:711-739, 2011

Physics

Mathematical Physics

29 pages. Version 2: Several sections and proofs were improved and completely rewritten. These include Sections 2.2.2,2.2.4 an

Scientific paper

10.1007/s00220-011-1277-y

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].

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