Logarithmic fluctuations for internal DLA

Authors:
David Jerison, Lionel Levine and Scott Sheffield

Journal:
J. Amer. Math. Soc. **25** (2012), 271-301

MSC (2010):
Primary 60G50, 60K35, 82C24

Published electronically:
August 15, 2011

MathSciNet review:
2833484

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Abstract | References | Similar Articles | Additional Information

Abstract: Let each of particles starting at the origin in perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set of occupied sites is (with high probability) close to a disk of radius . We show that the discrepancy between and the disk is at most logarithmic in the radius: i.e., there is an absolute constant such that with probability ,

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Additional Information

**David Jerison**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Email:
jerison@math.mit.edu

**Lionel Levine**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Email:
levine@math.mit.edu

**Scott Sheffield**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Email:
sheffield@math.mit.edu

DOI:
http://dx.doi.org/10.1090/S0894-0347-2011-00716-9

Received by editor(s):
December 3, 2010

Received by editor(s) in revised form:
July 8, 2011

Published electronically:
August 15, 2011

Additional Notes:
This work was supported by NSF grants DMS-1069225 and DMS-0645585 and an NSF Postdoctoral Research Fellowship.

Article copyright:
© Copyright 2011
David Jerison, Lionel Levine, and Scott Sheffield