Probability Seminar

A very large collection of spheres, such as a road bed of sand, can behave like ice, on which a heavy truck can drive, or like water, on which it would sink. The change in behavior is due to an immeasurable small feature, according to which the sphere packing is either frozen or melted. The mathematics has been a mystery for 200 years. The effect can supposedly be seen in Monte Carlo computer simulations, but can they be trusted? New developments in Markov processes may show the way forward.