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Communications in Mathematical Physics

, Volume 216, Issue 3, pp 583–607 | Cite as

Aggregation in the Plane and Loewner's Equation

  • L.  Carleson
  • N. Makarov

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.

Keywords

Differential Equation Phase Space Aggregation Process Loewner Chain Complex Analytic Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • L.  Carleson
    • 1
  • N. Makarov
    • 2
  1. 1.Royal Institute of Technology, Department of Mathematics, Stockholm, 10044, Sweden.¶E-mail: carleson@math.kth.seSE
  2. 2.California Institute of Technology, Department of Mathematics, Pasadena, CA 91125, USA.¶E-mail: makarov@cco.caltech.eduUS

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