Fast simulation of large‐scale growth models1. Issue 2 (23rd February 2012)

• Record Type: Journal Article
• Authors: Friedrich, Tobias; Levine, Lionel
• Is Part Of: Random structures & algorithms. Volume 42:Issue 2(2013)
• Page Start: 185
• Page End: 213
• Publication Date: 2012-02-23
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20412
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 approximation for the odometer, we successively correct under‐ and overestimates and provably arrive at the correct final state. Internal diffusion‐limited aggregation (IDLA) is one of the models amenable to our technique. The boundary fluctuations in IDLA were recently proved to be at most logarithmic in the size of the growth cluster, but the constant in front of the logarithm is still not known. As an application of our method, we calculate the size of fluctuations over two orders of magnitude beyond previous simulations, and use the results to estimate this constant. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012</p> </abstract>