Matthew Dickson

Emergence of random interlacements in interacting loop soups.

It is a famous conjecture of Feynman that the quantum mechanical phenomenon of Bose-Einstein Condensation in Bose gases corresponds to the emergence of `long loops' in appropriate loop soup ensembles. For the non-interacting Bose gas, it has been shown in previous work that the limiting measure of the loop soup gives rise to random interlacements. In this talk we will see how random interlacements can emerge in an interacting model that also highlights some of the current limitations of the approach. This talk will be based on joint work with Quirin Vogel (NYU Shanghai) and Stefan Adams (Warwick).