Colloquium on June 12, 2006

Lawrence S. Schulman
Martin-Gutzwiller Fellowship, Award Ceremony

Imaging dynamics: Phase transitions, clusters, and geometry from spectral analysis

The transient, ephemeral and unpredictable are often studied using stochastic dynamics. A central object for such dynamics is the matrix of transition probabilities. Spectral properties of this matrix encode a great deal of information about a system's behavior. I will show how this code can reveal the presence of phase transitions, how it can be used to provide a natural metric on the space (from which clusters and network properties can be obtained) and how, without reference to outside information, it can reveal the geometry of an underlying space for a stochastic process.