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Aggregation in the Plane and Loewner's Equation

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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.

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Authors and Affiliations

  1. Royal Institute of Technology, Department of Mathematics, Stockholm, 10044, Sweden.¶E-mail: carleson@math.kth.se, , , , , , SE

    L. Carleson

  2. California Institute of Technology, Department of Mathematics, Pasadena, CA 91125, USA.¶E-mail: makarov@cco.caltech.edu, , , , , , US

    N. Makarov

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  1. L. Carleson
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  2. N. Makarov
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Received: 2 May 2000 / Accepted: 5 September 2000

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Carleson, L., Makarov, N. Aggregation in the Plane and Loewner's Equation. Commun. Math. Phys. 216, 583–607 (2001). https://doi.org/10.1007/s002200000340

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  • DOI: https://doi.org/10.1007/s002200000340

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