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Growing random 3-connected maps or Comment s'enfuir de l'Hexagone


 
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1. Title Title of document Growing random 3-connected maps or Comment s'enfuir de l'Hexagone
 
2. Creator Author's name, affiliation, country Louigi Addario-Berry; McGill University; Canada
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random maps, random trees, random planar graphs, growth procedures
 
3. Subject Subject classification 60C05, 60J80, 05C10
 
4. Description Abstract We use a growth procedure for binary trees due to Luczak and Winkler, a bijection between binary trees and irreducible quadrangulations of the hexagon due to Fusy, Poulalhon and Schaeffer, and the classical angular mapping between quadrangulations and maps, to define a growth procedure for maps. The growth procedure is local, in that every map is obtained from its predecessor by an operation that only modifies vertices lying on a common face with some fixed vertex. As n tends to infinity, the probability that the n'th map in the sequence is 3-connected tends to 2^8/3^6. The sequence of maps has an almost sure limit G, and we show that G is the distributional local limit of large, uniformly random 3-connected graphs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSERC, FQRNT
 
7. Date (YYYY-MM-DD) 2014-08-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3314
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3314
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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