Abstract
A number of problems arise in mathematical physics which deal directly or indirectly with harmonic measure, i.e., with hitting probabilities of simple random walks. The more difficult problems involve understanding the nature of harmonic measure at points on fractal-like sets. We will describe a number of these problems in this paper — intersectionprobabilities of random walks; random walks grown using harmonic measure (loop-erased or Laplacian random walk); and clusters grown using harmonic measure (diffusion limited aggregation and related models). There is a large range of open problems in describing these random walks and clusters rigorously.
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© 1994 Springer Science+Business Media Dordrecht
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Lawler, G.F. (1994). Random Walks, Harmonic Measure, and Laplacian Growth Models. In: Grimmett, G. (eds) Probability and Phase Transition. NATO ASI Series, vol 420. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8326-8_11
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DOI: https://doi.org/10.1007/978-94-015-8326-8_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4370-2
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