Abstract ▼ AI-Helper

Abstract: We study an aggregation process which can be viewed as a deterministic analogue of the DLA model in the plane, or as a regularized version of the Hele-Shaw problem. The process is defined in terms of the Loewner differential equation. Using complex analytic methods, we establish a Kesten-t...

Abstract: We study an aggregation process which can be viewed as a deterministic analogue of the DLA model in the plane, or as a regularized version of the Hele-Shaw problem. The process is defined in terms of the Loewner differential equation. Using complex analytic methods, we establish a Kesten-type estimate for the growth of the cluster. We also indicate a real-variable approach based on a certain martingale structure in the phase space of the inverse Loewner chain.