Conformal Invariance, Droplets, And Entanglement

. 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 of these topics, as summarised here. Detailed bibliographies of recent work are included. 1. Introduction Rather than attempt to summarise the `state of the art' in percolation and disordered systems, a task for many volumes, we concentrate in this short article on three areas of recent progress, namely conformal invariance, droplets, and entanglement. In each case, the target is to stimulate via a brief survey, rather than to present the details. Much of the contents of this article may be expressed in terms of the randomcluster model, but for simplicity we consider here only the special case of percolation, defined as f..