Random Spatial Processes Program

In recent years probability theory has made immense progress in understanding the basic two-dimensional models of statistical mechanics and random surfaces. Prior to the 1990s the major interests and achievements of probability theory were with respect to one-dimensional objects: Brownian motion and stochastic processes, random trees, and the like. Inspired by work of physicists in the 1970s and 1980s on conformal invariance and field theories in two dimensions, a number of leading probabilists and combinatorialists began thinking about spatial process in two dimensions: percolation, polymers, dimer models, Ising models. Major breakthroughs by Kenyon, Schramm, Lawler, Werner, Smirnov, Sheffield, and others led to a rigorous underpinning of conformal invariance in two-dimensional systems and paved the way for a new era of two-dimensional probability theory.