Analysis and Probability Seminar

We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous mirror weights. In the terminology of quantum spins, this symmetry-breaking is called "dimerisation". Based on joint works with K. Ryan as well as with P. Muehlbacher, B. Nachtergaele and D. Ueltschi.