Logarithmic fluctuations from circularity

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Microsoft Research
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Published on ● Video Link: https://www.youtube.com/watch?v=8VQlMZM1Im8


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Vlog
Duration: 59:56
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Starting with n particles at the origin in Z^d, let each particle in turn perform simple random walk until reaching an unoccupied site. Lawler, Bramson and Griffeath proved that with high probability the resulting random set of n occupied sites is close to a ball. We show that its fluctuations from circularity are, with high probability, at most logarithmic in the radius of the ball, answering a question posed by Lawler in 1995 and confirming a prediction made by chemists Meakin and Deutch in the 1980's. Joint work with David Jerison and Scott Sheffield.



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