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L-Shapes for the Logarithmic η-Model for DLA in Three Dimensions

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Seminar on Stochastic Processes, 1991

Part of the book series: Progress in Probability ((PRPR,volume 29))

Abstract

There has been a lot of study recently of what can be called nearest neighbor cluster models. These are Markov chains A n , with state space of the set of finite connected subsets of the integer lattice Z d, A 1 = {0}, and such thatA n+1is obtained from A n by adding one point from the boundary of A n . In this paper we discuss a new result for one such model, a variant of diffusion limited aggregation (DLA) first studied by Kesten [2].

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References

  1. H. Kesten (1990). Upper bounds for the growth rate of DLA. Physica A 168 529–535.

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  2. H. Kesten (1991). Some caricatures of multiple contact diffusion-limited aggregation and the η-model, to appear in Proceedings of Durham Symposium on Stochastic Analysis.

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  3. G. Lawler (1991). Intersections of Random Walks. Birkäuser Boston.

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  4. G. Lawler (1991). Escape probabilities for slowly recurrent sets, to appear.

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  5. F. Spitzer (1976). Principies of Random Walk. Springer-Verlag.

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  6. T. Vicsek (1989). Fractal Growth Phenomena. World Scientific.

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  7. T. Witten and L. Sander (1981). Diffusion-limited aggregation, a kinetic growth phenomenon. Phys. Rev. Lett. 47 1400–1403.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27706, USA

    Gregory F. Lawler

Authors
  1. Gregory F. Lawler
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Editor information

Editors and Affiliations

  1. Dept. of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 08544, USA

    E. Çinlar

  2. Dept. of Mathematics, Stanford University, Stanford, CA, 94305, USA

    K. L. Chung

  3. Dept. of Mathematics, University of California-San Diego, La Jolla, CA, 92093, USA

    M. J. Sharpe  & P. J. Fitzsimmons  & 

  4. Dept. of Mathematics, University of California, Los Angeles, CA, 90024, USA

    S. Port  & T. Liggett  & 

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© 1992 Springer Science+Business Media New York

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Lawler, G.F. (1992). L-Shapes for the Logarithmic η-Model for DLA in Three Dimensions. In: Çinlar, E., Chung, K.L., Sharpe, M.J., Fitzsimmons, P.J., Port, S., Liggett, T. (eds) Seminar on Stochastic Processes, 1991. Progress in Probability, vol 29. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0381-0_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0381-0_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6735-5

  • Online ISBN: 978-1-4612-0381-0

  • eBook Packages: Springer Book Archive

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