Critical Behaviour in Hierarchical Percolation - Statistical Mechanics Models

Explore critical behavior in hierarchical percolation through this 51-minute lecture by Tom Hutchcroft at the USC Probability and Statistics Seminar. Delve into the fascinating world of statistical mechanics models undergoing phase transitions, examining their fractal-like behavior at critical points. Learn about critical exponents and their role in describing power-law growth or decay of various quantities of interest. Discover how these exponents are expected to depend on dimension but not on microscopic model details. Gain insights into the progress made in understanding two-dimensional and high-dimensional models over the past three decades, while recognizing the ongoing mysteries surrounding intermediate dimensions like three. Focus on hierarchical percolation as a simplified version of percolation on Z^d, and explore Hutchcroft's forthcoming work that provides a comprehensive description of critical behavior across all dimensions.