Abstract: We introduce a random walk loop soup which reduces to or is related to several models of interest in statistical mechanics, including the Spin O(N) model, the Bose gas, the dimer model, the double dimer model, random lattice permutations. The main questions involve the characterisation of the size and the geometry of the loops, which interact by mutual repulsion. We present some results about the existence of macroscopic loops in three and higher dimensions and some more recent results on the absence of macroscopic loops in two dimensional (not necessarily planar) graphs.
Random walk loops, dimers and spins
29.05.2024 15:00 - 16:30
Organiser:
M. Lis, W. da Silva
Location: