These lecture notes provide a pedagogical tour of random walk and random graph theory, covering standard results without claiming new research advances.
An introduction to Galton-Watson trees and their local limits
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abstract
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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2024 1verdicts
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A random walk among random graphs
These lecture notes provide a pedagogical tour of random walk and random graph theory, covering standard results without claiming new research advances.