The Bernouilli percolation model has been intensely investigated for over 50 years yet keeps yielding new exact results. The model will be introduced and some recent work will be reviewed, including the recent history of the crossing problem first studied by Cardy and by Langlands and co-workers, and more recently rigorously solved by Schramm and Werner (the recent Fields medalist). In recent work with Peter Kleban, we have found explicit expressions for density profiles and a surprising superposition property for clusters that touch two points on a boundary. In other recent work with Christian Scullard, we have found a kind of generalization of the star-triangle transformation (independently found by Lincoln Chayes at about the same time) and show how it can be used to find transition points of a wide variety of new lattices.
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