Transient random walks in random environment on a Galton–Watson tree

By Elie Aidékon. 2007

51 citations recorded by the source corpus.

We consider a transient random walk (Xn) in random environment on a Galton–Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that Xn is of order of magnitude nΛ, with $${\Lambda \in (0,1)}$$. We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, which improves a recent result of Collevecchio (Probab Theory Related 136(1):81–101, 2006).

Subfields: Condensed Matter Physics, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/bd47a306878c3793a8c0b426dfebf9c3630e0db7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Russell Lyons
2. Zhan Shi
3. Yuval Peres
4. Thomas Madaule
5. Wendelin Werner
6. Elie Aidékon
7. Alexei Borodin
8. Ben Morris

In Mathematical Physics

1. Zhan Shi
2. Russell Lyons
3. Yuval Peres
4. Alexei Borodin
5. Pablo Shmerkin
6. Charles Bordenave
7. Pietro Caputo
8. Michael Hochman

In Molecular Biology

1. Yuval Peres
2. Russell Lyons
3. Zhan Shi

Citations in the corpus

• Branching random walks (2015, background): “In the sub-ballistic case, the escape rate is also studied in [5].”
• Probability on Trees and Networks (2017, background): “, Aizenman and Lebowitz (1988), Schonmann (1992), Holroyd (2003), Adler and Lev (2003), Gravner and Holroyd (2009), Balogh, Bollobás, and Morris (2009), Balogh, Bollobás, Duminil-Copin, and Morris (2011)).”