Alan Sola

Scaling limits of anisotropic Hastings–Levitov clusters

We consider a variation of the standard Hastings-Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations around the deterministic limit flow.

CYCLICITY IN DIRICHLET-TYPE SPACES AND EXTREMAL POLYNOMIALS

For functions f in Dirichlet-type spaces

Expected discrepancy for zeros of random algebraic polynomials

{D_\alpha }

Norm expansion along a zero variety

, we study how to determine constructively optimal polynomials pn that minimize

Derivatives of rational inner functions: geometry of singularities and integrability at the boundary

{\left\| {pf - 1} \right\|_\alpha }

Multi-parameter extensions of a theorem of Pichorides

among all polynomials p of degree at most n. We then obtain sharp estimates for the rate of decay of