Abstract: We study two different double dimer models which, along with the usual non-crossing loops and coubled edges, exhibit arcs which begin and end at a certain portion of the boundary. We argue that these models satisfy a discrete version of a coupling between the Arc Loop Ensemble (ALE) and two Gaussian Free Fields with different boundary conditions. We prove that certain statistics of the arcs are conformally invariant in the small mesh limit, giving the same limit from both discrete models, and equal to the corresponding ALE statistics.
Joint work with Marcin Lis and Lucas Rey.
Conformally invariant boundary arcs in double dimer models
04.11.2024 17:00 - 18:00
Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
Location:
HS 42, Hauptgebäude UNIVIE, 2. Stock, Stiege 7