Bertoin, Jean (2013). Almost giant clusters for percolation on large trees with logarithmic heights. Journal of Applied Probability, 50(3):603-611.
This paper is based on works presented at the 2012 Applied Probability Trust Lecture in Sheffield; its main purpose is to survey the recent asymptotic results of Bertoin (2012a) and Bertoin and Uribe Bravo (2012b) about Bernoulli bond percolation on certain large random trees with logarithmic height. We also provide a general criterion for the existence of giant percolation clusters in large trees, which answers a question raised by David Croydon.
This paper is based on works presented at the 2012 Applied Probability Trust Lecture in Sheffield; its main purpose is to survey the recent asymptotic results of Bertoin (2012a) and Bertoin and Uribe Bravo (2012b) about Bernoulli bond percolation on certain large random trees with logarithmic height. We also provide a general criterion for the existence of giant percolation clusters in large trees, which answers a question raised by David Croydon.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Language: | English |
| Date: | 2013 |
| Deposited On: | 22 Nov 2013 11:31 |
| Last Modified: | 24 Sep 2019 19:46 |
| Publisher: | Applied Probability Trust |
| ISSN: | 0021-9002 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1239/jap/1378401225 |
Bertoin, Jean