The continuous limit of large random planar maps
We discuss scaling limits of random planar maps chosen uniformly over the set of all $2p$-angulations with $n$ faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space. Although we are not able to prove the uniqueness of the distribution of the...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2008-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3554/pdf |
| _version_ | 1797270428637462528 |
|---|---|
| author | Jean-François Le Gall |
| author_facet | Jean-François Le Gall |
| author_sort | Jean-François Le Gall |
| collection | DOAJ |
| description | We discuss scaling limits of random planar maps chosen uniformly over the set of all $2p$-angulations with $n$ faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space. Although we are not able to prove the uniqueness of the distribution of the Brownian map, many of its properties can be investigated in detail. In particular, we obtain a complete description of the geodesics starting from the distinguished point called the root. We give applications to various properties of large random planar maps. |
| first_indexed | 2024-04-25T02:04:07Z |
| format | Article |
| id | doaj.art-8a4675e24c1042bcb4f33fe52aa1a6b6 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:04:07Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8a4675e24c1042bcb4f33fe52aa1a6b62024-03-07T14:36:57ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AI,...Proceedings10.46298/dmtcs.35543554The continuous limit of large random planar mapsJean-François Le Gall0Département de Mathématiques [ORSAY]We discuss scaling limits of random planar maps chosen uniformly over the set of all $2p$-angulations with $n$ faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space. Although we are not able to prove the uniqueness of the distribution of the Brownian map, many of its properties can be investigated in detail. In particular, we obtain a complete description of the geodesics starting from the distinguished point called the root. We give applications to various properties of large random planar maps.https://dmtcs.episciences.org/3554/pdfgeodesicstopological typeplanar mapsscaling limitsrandom treesgromov-hausdorff distancehausdorff dimension[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-ds] mathematics [math]/dynamical systems [math.ds][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Jean-François Le Gall The continuous limit of large random planar maps Discrete Mathematics & Theoretical Computer Science geodesics topological type planar maps scaling limits random trees gromov-hausdorff distance hausdorff dimension [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-ds] mathematics [math]/dynamical systems [math.ds] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | The continuous limit of large random planar maps |
| title_full | The continuous limit of large random planar maps |
| title_fullStr | The continuous limit of large random planar maps |
| title_full_unstemmed | The continuous limit of large random planar maps |
| title_short | The continuous limit of large random planar maps |
| title_sort | continuous limit of large random planar maps |
| topic | geodesics topological type planar maps scaling limits random trees gromov-hausdorff distance hausdorff dimension [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-ds] mathematics [math]/dynamical systems [math.ds] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3554/pdf |
| work_keys_str_mv | AT jeanfrancoislegall thecontinuouslimitoflargerandomplanarmaps AT jeanfrancoislegall continuouslimitoflargerandomplanarmaps |