logarithmic fluctuations
Recently Published Documents


TOTAL DOCUMENTS

2
(FIVE YEARS 0)

H-INDEX

1
(FIVE YEARS 0)

2012 ◽  
Vol 25 (1) ◽  
pp. 271-301 ◽  
Author(s):  
David Jerison ◽  
Lionel Levine ◽  
Scott Sheffield


2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.



Sign in / Sign up

Export Citation Format

Share Document