A balanced excited random walker returns home
Title: Balanced Excited Random Walk in Two Dimensions Authors and Year: Omer Angel, Mark Holmes, Alejandro Ramirez; 2023 Journal: Annals of Probability Will balance and excitement always lead a random walker home? A new paper in the Annals of Probability attempts to answer this question and explores paths along the way. Random Walks Imagine you moved into a new neighborhood and you are excited to go on a walk to explore. The neighborhood is arranged in a grid structure, so at each intersection you have four choices for which direction to take: left, right, forwards, or backwards. Since you don’t know where you’re going, you decide to use some randomness to pick which direction to take. This is a random walk: a type of random process that is just a succession of steps on some sort of graph according to some probabilistic rules. The neighborhood grid gives a walk in…