Some remarks on Laplacian growth

The Hastings–Levitov process HL ( α ) describes planar random compact subsets by means of random compositions of conformal maps. We prove the existence of the scaling limit of HL ( 0 ) and show that the limit sets are one-dimensional. We also give estimates for the dimension of HL ( α ) for 0 < α ⩽ 2 , and discuss scaling limits of deterministic variants.