Random skew plane partitions with a piecewise periodic back wall
Résumé
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571-609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571-609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107-142, 2009) appearing in the asymptotics at the top of the limit shape.