Back to Search
Start Over
Generalized range of slow random walks on trees
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- In this work, we are interested in the set of visited vertices of a tree $\mathbb{T}$ by a randomly biased random walk $\mathbb{X}:=(X_n,n \in \mathbb{N})$. The aim is to study a generalized range, that is to say the volume of the trace of $\mathbb{X}$ with both constraints on the trajectories of $\mathbb{X}$ and on the trajectories of the underlying branching random potential $\mathbb{V}:=(V(x), x \in \mathbb{T})$. Focusing on slow regime's random walks (see [HS16b], [AC18]), we prove a general result and detail examples. These examples exhibit many different behaviors for a wide variety of ranges, showing the interactions between the trajectories of $\mathbb{X}$ and the ones of $\mathbb{V}$.<br />Comment: 58 pages
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....47b7f4b0eddad9cd7855f75c71004ea7
- Full Text :
- https://doi.org/10.48550/arxiv.2111.05029