Fast simulation of large-scale growth models

We give 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 internal diffusion-limited aggregation 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 are logarithmic in the radius.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Tobias Friedrich, Lionel Levine
• Keywords: Certain Growth Models, CORR 2010, Correct Final State, Education, Final State