The Library
Central limit theorem for first-passage percolation time across thin cylinders
Tools
Chatterjee, Sourav and Dey, Partha S. (2013) Central limit theorem for first-passage percolation time across thin cylinders. Probability Theory and Related Fields, Volume 156 (Number 3-4). pp. 613-663. doi:10.1007/s00440-012-0438-z ISSN 0178-8051.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s00440-012-0438-z
Abstract
We prove that first-passage percolation times across thin cylinders of the form [0, n] × [−h n , h n ] d-1 obey Gaussian central limit theorems as long as h n grows slower than n 1/(d+1). It is an open question as to what is the fastest that h n can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | August 2013 | ||||
Dates: |
|
||||
Volume: | Volume 156 | ||||
Number: | Number 3-4 | ||||
Page Range: | pp. 613-663 | ||||
DOI: | 10.1007/s00440-012-0438-z | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |