Geneva mathematical physics seminar

Mondays at 4.15pm in room 1.15.

Upcoming seminar:

Monday 29th of April: Réka Szabó (Paris Dauphine) 

Stability results for random monotone cellular automata 

Abstract: In a monotone cellular automaton, each site in the d-dimensional integer lattice can at each integer time take the values zero or one. The value of a site at a given time is a monotone function of the values of the site and finitely many of its neighbours at the previous time. Toom’s stability theorem gives necessary and sufficient conditions for the all one state to be stable under small random perturbations. We review Toom’s Peierls argument and extend it to random cellular automata, in which the functions that determine the value at a given space-time point are random and i.i.d. We are especially interested in the case where with positive probability, the identity map is applied. Being able to include this map is important for understanding continuous-time interacting particle systems that can be seen as limits of discrete-time cellular automata. We derive sufficient conditions for the stability of such random cellular automata. Joint work with Cristina Toninelli and Jan Swart. 

Tuesday 30th of April, 15h15, room 1.15: Frank Ferrari (Université Libre de Bruxelles)

 Jackiw-Teitelboim Gravity, Random Disks of Constant Curvature, Self-Overlapping Curves and Liouville CFT1

Abstract: Jackiw-Teitelboim quantum gravity is a model of two-dimensional gravity for which the bulk curvature is fixed but the extrinsic curvature of the boundaries is free to fluctuate. The negative curvature model has been studied extensively in the recent physics literature, in a particular ``Schwarzian'' limit, because of its relevance in describing quantum black holes and their SYK-like duals.

A first-principle approach reveals that the description used in the literature so far is an effective theory valid on distances much larger than the curvature length scale of the bulk geometry.

At the microscopic level, the theory should be defined by taking the continuum limit of a new model of random polygons. The polygons, called ``self-overlapping,'' are constrained to bound a disk immersed in the plane. They must be counted with an appropriate multiplicity. The solution of the model could be found in principle by solving a difficult ``dually weighted’' Hermitian matrix model.

Motivated by standard heuristic path integral arguments, mimicking similar arguments used for Liouville gravity in the 80s and the 90s, we conjecture that an equivalent description is obtained in terms of a boundary log-correlated field. This yields predictions for the critical exponents of the self-overlapping polygon models and open the path to a wide range of potential applications.

Contact:

 trishen.gunaratnam@unige.ch / romain.panis@unige.ch / alexis.prevost@unige.ch