Final Report Summary - RIMACO (Rigorous Mathematical Connections between the Theory of Computations and Statistical Physics)
The project studies probabilistic algorithms using ideas of statistical physics. One main conclusion of the project is that a geometric phenomenon known as "shattering", a massive, rapid change in the geometry of the set of solutions of a problem, represents a potential barrier to efficient computation. In particular, the project provides strong evidence that either this barrier is insurmountable, or that significantly new ideas will be needed in algorithm design to overcome it. Another main conclusion is the formulation of local conditions under which probabilistic dynamics will allow a large system to quickly reach a minimum energy state.