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AG Audience

English

30 Minutes

Saarbrücken

This talk explains the new colorful piece of art which was put up on our floor a few weeks ago. More precisely, I present an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process. Starting from an educated guess for the odometer, we successively correct under- and overestimates and provably arrive at the correct final state. The degree of speedup depends on the accuracy of the initial guess.

Determining the size of the boundary fluctuations in growth models like internal diffusion-limited aggregation (IDLA) is a long-standing open problem in statistical physics. As an application of our method, we calculate the size of fluctuations over two orders of magnitude beyond previous simulations. Our data strongly support the conjecture that the fluctuations of IDLA are logarithmic in the radius.

This is joint work with Lionel Levine (MIT).

Tobias Friedrich

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