Abstract: The double dimer model (DDM) on a planar graph is a model of random loops, and the Gaussian free field (GFF) is a model of a height function. The two models are linked by a conjecture that the DDM loops converge in the scaling limit to loops in the continuum, which are level lines of the GFF.
The DDM has fermionic features, in that certain correlations can we written as determinants, whereas the GFF is a boson. I will highlight these two contrasting features appearing in the same context. In the process, certain crossing probabilities in the DDM can be computed exactly, and analogous computations can be done for the metric graph GFF, a discrete analogue of the GFF. These computations yield the same result, giving some evidence of the aforementioned conjecture.
This is joint work with Marcin Lis.
Fermionic and bosonic features of the double dimer model and the Gaussian free field
06.10.2022 14:00 - 16:00
Organiser:
Marcin Lis (TU Wien)
Location:
TU Wien, EI 6 Eckert HS, 4. OG, Gußhausstraße 25-29, 1040 Wien