Logarithmic fluctuations from circularity

  • Lionel Levine | Cornell

Starting with n particles at the origin in Zd, 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.

Speaker Details

Lionel Levine is an Assistant Professor at Cornell. He obtained his PhD from UC Berkeley in 2008, and was a postdoctoral Researcher at MIT.

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      Jeff Running

Series: Microsoft Research Talks