Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewn...

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent z=1. The events that occur are adsorption, which is local, and desorption which is nonlocal and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the c=0 logarithmic conformal field theory of percolation. This im...

The study of dynamics in the plane has recently seen a surge in interest due to three recent breakthroughs: the Sullivan-McMullen-Lyubich proof of the Feigenbaum Universality, the introduction by O. Schramm of SLE processes, and the work of S. Smirnov on percolation. The fields of Holomorphic Dynamics, SLE, and Conformal Field Theory (CFT) are now seen to be closely linked, the glue being provi...

It is proved that in the Voronoi model for percolation in dimension 2 and 3, the crossing probabilities are asymptotically invariant under conformal change of metric. To deene Voronoi percolation on a manifold M , you need a measure , and a Riemannian metric ds. Points are scattered according to a Poisson point process on (M;), with some density. Each cell in the Voronoi tessellation determined...

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in...

This short survey is written by a physicist. It contains neither theorems nor precise definitions. Its main content is a description of the results of numerical solution of the equations of fluid mechanics in the regime of developed turbulence. Due to limitations of computers, the results are not very precise. Despite being neither exact nor rigorous, the findings may nevertheless be of interes...

Geoffrey Grimmett Abstract. Very brief surveys are presented of three topics of importance for interacting random systems, namely conformal invariance, droplets, and entanglement. For ease of description, the emphasis throughout is upon progress and open problems for the percolation model, rather than for the more general random-cluster model. Substantial recent progress has been made on each o...

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find t...