Date: Friday, March 18, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Lozenge tilings with gaps in a 90 degree wedge domain with mixed boundary conditions
Abstract: We consider a triangular gap of side two in a 90 degree
angle on the triangular lattice with mixed boundary conditions: a
constrained, zigzag boundary along one side, and a free lattice line
boundary along the other. We study the interaction of the gap with the
corner as the rest of the angle is completely filled with lozenges. We
show that the resulting correlation is governed by the product of the
distances between the gap and its three images in the sides of the
angle. This provides evidence for a unified way of understanding the
interaction of gaps with the boundary under mixed boundary conditions,
which we present as a conjecture. Our conjecture is phrased in terms
of the steady state heat flow problem in a uniform block of material
in which there are a finite number of heat sources and sinks. This new
physical analogy is equivalent in the bulk to the electrostatic
analogy we developed in previous work, but arises as the correct one
for the correlation with the boundary.
Files:
Speaker: Mihai Ciucu
Institution: U. Indiana
Event Organizer: Sergey Fomin
