7 papers
On the Loewner energy of a welding homeomorphism
Shuo Fan, Fredrik Viklund, Yilin Wang
To any Jordan curve one may associate a circle homeomorphism via conformal welding. Through this correspondence, the Loewner energy , also kno…
Dyson Brownian motion on a Jordan curve
Vladislav Guskov, Mingchang Liu, Fredrik Viklund
Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss…
Loewner--Kufarev entropy and large deviations of the Hastings--Levitov model
Nathanaël Berestycki, Vladislav Guskov, Fredrik Viklund
We consider the Hastings--Levitov HL(0) model in the small particle scaling limit and prove a large deviation principle. The rate function is given by the relative entropy of the d…
Planar Coulomb gas on a Jordan arc at any temperature
Klara Courteaut, Kurt Johansson, Fredrik Viklund
We study a planar Coulomb gas confined to a sufficiently smooth Jordan arc in the complex plane, at inverse temperature . Let \[\bar{Z}_{n}^β(γ) = Z_{n}^β(γ)/\left(2 \tex…
Current expansion and couplings for Ising lattice gauge theory
Malin P. Forsström, Fredrik Viklund
In this note, we discuss a random current expansion and a switching lemma for Ising lattice gauge theory at all choices of inverse temperature , leading to summation over surfac…
Competitive Hele-Shaw flow and quadratic differentials
Fredrik Viklund, David Witt Nyström
We introduce and investigate a generalization of the Hele-Shaw flow with injection where several droplets compete for space as they try to expand due to internal pressure while sti…
Coulomb gas and the Grunsky operator on a Jordan domain with corners
Kurt Johansson, Fredrik Viklund
Let be a Jordan domain of unit capacity. We study the partition function of a planar Coulomb gas in with a hard wall along , \[Z_{n}(D) =\frac 1{n!}\int_{D^n…