The Library
Expansion of percolation critical points for Hamming graphs
Tools
Federico, Lorenzo, Van Der Hofstad, Remco , Den Hollander, Frank and Hulshof, Tim (2020) Expansion of percolation critical points for Hamming graphs. Combinatorics, Probability and Computing, 29 (1). pp. 68-100. doi:10.1017/S0963548319000208 ISSN 0963-5483.
|
PDF
WRAP-expansion-percolation-critical-points-hamming-graphs-Federico-2019.pdf - Accepted Version - Requires a PDF viewer. Download (974Kb) | Preview |
Official URL: https://doi.org/10.1017/S0963548319000208
Abstract
The Hamming graph H(d, n) is the Cartesian product of d complete graphs on n vertices. Let be the degree and be the number of vertices of H(d, n). Let be the critical point for bond percolation on H(d, n). We show that, for fixed and ,
which extends the asymptotics found in [10] by one order. The term is the width of the critical window. For we have , and so the above formula represents the full asymptotic expansion of . In [16] we show that this formula is a crucial ingredient in the study of critical bond percolation on H(d, n) for . The proof uses a lace expansion for the upper bound and a novel comparison with a branching random walk for the lower bound. The proof of the lower bound also yields a refined asymptotics for the susceptibility of a subcritical Erdös–Rényi random graph
Item Type: | Journal Article | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Random graphs, Probabilities | ||||||||||||
Journal or Publication Title: | Combinatorics, Probability and Computing | ||||||||||||
Publisher: | Cambridge University Press | ||||||||||||
ISSN: | 0963-5483 | ||||||||||||
Official Date: | January 2020 | ||||||||||||
Dates: |
|
||||||||||||
Volume: | 29 | ||||||||||||
Number: | 1 | ||||||||||||
Page Range: | pp. 68-100 | ||||||||||||
DOI: | 10.1017/S0963548319000208 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | © Cambridge University Press 2019 | ||||||||||||
Date of first compliant deposit: | 21 August 2019 | ||||||||||||
Date of first compliant Open Access: | 5 February 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year