An introduction to Galton-Watson trees and their local limits
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866910608226516992 |
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| author | Abraham, Romain Delmas, Jean-François |
| author_facet | Abraham, Romain Delmas, Jean-François |
| contents | The aim of this lecture is to give an overview of old and new resultson Bienaymé-Galton-Watson (BGW) trees. After introducing the framework of discretetrees, we first give alternative proofs of classical results on theextinction probability of BGW processes and on thedescription of the processes conditioned on extinction or onnon-extinction. Then, we study recent local limits of critical orsub-critical BGW trees conditioned to be large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_05571 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | An introduction to Galton-Watson trees and their local limits Abraham, Romain Delmas, Jean-François Probability The aim of this lecture is to give an overview of old and new resultson Bienaymé-Galton-Watson (BGW) trees. After introducing the framework of discretetrees, we first give alternative proofs of classical results on theextinction probability of BGW processes and on thedescription of the processes conditioned on extinction or onnon-extinction. Then, we study recent local limits of critical orsub-critical BGW trees conditioned to be large. |
| title | An introduction to Galton-Watson trees and their local limits |
| topic | Probability |
| url | https://arxiv.org/abs/1506.05571 |