Scaling Exponents in Stationary Random Graphs

Explore scaling exponents in stationary random graphs in this 55-minute lecture presented by James Lee from the University of Washington at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the relationships between fractal dimension, walk dimension, resistance exponent, spectral dimension, and extremal growth exponent in random geometries. Examine the "Einstein relations" in the recurrent regime and discover how density and conductivity of stationary random graphs determine random walk escape rates and spectral dimension. Investigate the connection between spectral dimension and extremal volume growth exponent under weak spectral concentration conditions. Gain insights into statistical physics and random graph theory from this advanced mathematical presentation recorded on May 7, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.