I will discuss the asymptotics of the partition function of a planar Coulomb gas confined to an analytic Jordan arc. The asymptotics is given in terms of a Fredholm determinant of an operator called the arc-Grunsky operator that we introduce. It can also be expressed in terms of appropriate conformal maps. The sitaution is similar, but also different, to that of a Coulomb gas on a Jordan curve which relates to the Loewner energy of the curve. In the talk I will outline some of the arguments in the proof. This is joint work with Klara Courteaut and Fredrik Viklund.
Back to New Interactions between probability and geometry
Copyright. All Rights Reserved.