The Tree Builder Random Walk

In this presentation we will talk about a class of random walks that build their own domain. I.e., at each step of the random walk, the walker may add new vertices to the underlying graph according to some distribution. We will see that under the right conditions the walker might be either transient or recurrent. Additionally, in the transient regiment, the walker may exhibit ballistic behavior. We will also discuss some results from the perspective of the environment. That is, we will answer some questions regarding structural properties of the sequence of random graphs generated by the walker.