From Random Interlacements to Coordinate Percolation

In recent years remarkable progress was made in studies of various systems arising in theoretical computer science, mathematical biology, and statistical mechanics, all of which in one way or another could be reduced to percolative systems with long (infinite) range of interactions. Among others it includes Random Interlacement Process, Scheduling of random walks and coordinate percolation of Winkler. During my talk I will discuss some recent progress in studies of connectivity properties of such systems.