[Seminar] The SOKOBAN random walk by Ofek Lauber Bonomo
Random motion in disordered media is sensitive to the presence of obstacles, preventing atoms, molecules, and other particles from moving freely in space. When obstacles are static, a sharp transition between confined motion and free diffusion occurs at a critical obstacle density: the percolation threshold. In this talk, I introduce the Sokoban random walk, which is a new type of random walk, designed to test if this conventional wisdom continues to hold in the presence of simple tracer-media interactions. Akin to the protagonist of an eponymous video game , the Sokoban has some ability to push away obstacles that block its path. I show that while one expects this will allow the Sokoban to venture further away, it is surprisingly not always the case. Indeed, as it moves – pushing obstacles around – the Sokoban dynamically confines itself to a finite region whose mean size is uniquely determined by the initial obstacle density  . This finding breaks from the ruling “ant in a labyrinth” paradigm, vividly illustrating that even weak and localized tracer-media interactions cannot be neglected when coming to understand transport phenomena.
 Sokoban: https://www.mathsisfun.com/games/sokoban.html
 Bonomo, O.L. and Reuveni, S., 2022. Loss of Percolation Transition in the Presence of Simple Tracer-Media Interactions. arXiv preprint arXiv:2210.04343.