scholarly journals A quenched functional central limit theorem for planar random walks in random sceneries

2014 ◽  
Vol 19 (0) ◽  
Author(s):  
Nadine Guillotin-Plantard ◽  
Julien Poisat ◽  
Renato Soares dos Santos
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Functional Central Limit Theorem ◽  
Functional Central Limit

scholarly journals A quenched central limit theorem for biased random walks on supercritical Galton–Watson trees

2018 ◽  
Vol 55 (2) ◽  
pp. 610-626 ◽  
Author(s):  
Adam Bowditch
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Upper Bound ◽  
Functional Central Limit Theorem ◽  
Biased Random Walk ◽  
Quenched Central Limit Theorem ◽  
Functional Central Limit

AbstractIn this paper we prove a quenched functional central limit theorem for a biased random walk on a supercritical Galton–Watson tree with leaves. This extends a result of Peres and Zeitouni (2008) where the case without leaves was considered. A conjecture of Ben Arous and Fribergh (2016) suggests an upper bound on the bias which we observe to be sharp.

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