Sarai Hernandez Torres

Random interlacements is a Poissonian soup of doubly-infinite random walk trajectories on Z^d, with a parameter u > 0 controlling the intensity of the Poisson point process. In a natural way, the model defines a percolation on the edges of Z^d with...

Chase-escape is a competitive growth process in which red particles spread to adjacent uncoloured sites while blue particles overtake and kill adjacent red particles. We can think of this model as prey escaping from pursuing predators. If the red...

Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using loop-erased random walks. This connection gives a tractable method to study the UST. The strategy has been fruitful for scaling limits of the UST in the planar...