Stability and Chaos in Dynamical Last Passage Percolation
Explore the intricate world of statistical mechanics in this 50-minute lecture on stability and chaos in dynamical last passage percolation. Delve into the complex energy landscapes of statistical mechanical models, examining the ground state and near-ground states in systems like spin glasses and Gaussian polymers. Investigate the phenomenon of chaos and its relationship to the abundance of competing minimizers. Learn about recent research on a natural dynamics for planar last passage percolation, including quantified analysis of close energy rivals to the ground state. Discover the scale at which the transition from stability to chaos occurs in the dynamical model. Gain insights into the probabilistic and geometric techniques used, including harmonic analytic methods and Brownian Gibbs resampling analysis for random curve ensembles associated with last passage percolation through the Robinson-Schensted-Knuth correspondence.