Phase transition in reinforced random walk and RWRE on trees

@article{Pemantle1988PhaseTI,
  title={Phase transition in reinforced random walk and RWRE on trees},
  author={Robin Pemantle},
  journal={Annals of Probability},
  year={1988},
  volume={16},
  pages={1229-1241}
}
  • R. Pemantle
  • Published 1 July 1988
  • Mathematics
  • Annals of Probability
On donne a une marche aleatoire sur un arbre infini une sorte particuliere de retroaction positive de telle sorte que les aretes deja traversees aient plus de chances d'etre traversees dans le futur. On utilise la theorie de l'echangeabilite pour montrer que le processus est equivalent a une marche aleatoire dans un environnement aleatoire 
On some generalized reinforced random walk on integers
We consider Reinforced Random Walks where transitions probabilities are a function of the proportions of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase
Critical Random Walk in Random Environment on Trees of Exponential Growth
This paper studies the behavior of RWRE on trees in the critical case left open in previous work. For trees of exponential growth, a random perturbation of the transition probabilities can change a
Correction: Random walk in a random environment and first-passage percolation on trees
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a
Marches aléatoires en environnement aléatoire faiblement elliptique
Cette these est dediee a l'etude des marches aleatoires en milieu aleatoire sur Zd. On s'interesse tout particulierement aux environnements qui sont elliptiques, mais pas uniformement elliptiques, et
The Branching‐Ruin Number and the Critical Parameter of Once‐Reinforced Random Walk on Trees
The motivation for this paper is the study of the phase transition for recurrence/ transience of a class of self‐interacting random walks on trees, which includes the once‐reinforced random walk. For
Edge oriented reinforced random walks and RWRE
Submitted to the Annals of Probability PHASE TRANSITION FOR THE ONCE-REINFORCED RANDOM WALK ON Z D-LIKE TREES
In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we
Limit theorems for reinforced random walks on certain trees
Consider a linearly edge-reinforced random walk defined on the b-ary tree, b≥70. We prove the strong law of large numbers for the distance of this process from the root. We give a sufficient
Critical RWRE on trees and tree-indexed random walks
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the
...
...