The Abelian sandpile model on a graph G is a Markov chain whose state space is a subset of the set of functions with integer values defined on the vertices of G. The set of recurrent states of this Markov chain is called the sandpile group and the Abelian sandpile model can be then viewed […]

In 2001 Bolthausen, den Hollander and van den Berg obtained the asymptotics of the probability that the volume of a Wiener sausage at time t is smaller than expected by a fixed muliplicative constant. This asymptotics was given by a variational formula and they conjectured that the best strategy to achieve such a large deviation […]

Interacting Bose gas at zero temperature is often described by the Bogoliubov approximation. It involves quasiparticles, called phonons, with a rather curious dispersion relation responsible for superfluidity. The Fermi Golden Rule predicts that the lifetime of phonons is proportional to the 5th inverse power of momentum. This was first computed by Beliaev and goes under […]