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An introduction to Galton-Watson trees and their local limits

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arxiv 1506.05571 v3 pith:M4NVNCCM submitted 2015-06-18 math.PR

classification math.PR
keywords treesconditionedgivelimitslocalprocessesalternativebienaym
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The aim of this lecture is to give an overview of old and new resultson Bienaym\'e-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.

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