Random geometry and quantum gravity

Liste des Contributions

1. Hamiltonian Paths on Random Planar Maps

Bertrand Duplantier (Institut de Physique Théorique, Université Paris-Saclay)

12/02/2025 13:30

Hamiltonian paths are self-avoiding random walks that visit all sites of a given lattice. We consider various configuration exponents of Hamiltonian walks drawn on random planar maps. Estimates from exact enumerations are compared with predictions based on the Knizhnik-Polyakov-Zamolodchikov (KPZ) relations, as applied to exponents on the regular hexagonal lattice. Astonishingly, when the maps...

3. The chemical distance metric for non-simple CLE

Yizheng Yuan (Statistical Laboratory, Cambridge University, UK)

12/02/2025 15:00

We construct the continuum analogue of the chemical distance metric in
lattice models such as percolation. The chemical distance metric is the
graph distance induced by the percolation clusters. It is known that for
critical percolation, the lengths have non-trivial scaling behaviour,
however it is very difficult to find the exact scaling exponent. (This
is one of the questions from...

2. Interface scaling limit for the critical planar Ising model perturbed by a magnetic field

Léonie Papon (Durham University, UK)

12/02/2025 16:15

In this talk, I will consider the interface separating +1 and -1 spins in the critical planar Ising model with Dobrushin boundary conditions perturbed by an external magnetic field. I will prove that this interface has a scaling limit. This result holds when the Ising model is defined on a bounded and simply connected subgraph of $\delta\mathbb{Z}^2$, with $\delta > 0$. I will show that if the...