Minimal Surfaces in Random Environment

Explore a 50-minute lecture on Minimal Surfaces in Random Environment (MSRE) presented by Ron Peled from Tel Aviv University at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the fascinating world of surfaces that minimize both elastic energy and environmental potential energy, subject to specific boundary conditions. Discover the connections between MSRE and disordered spin systems, first-passage percolation models, and minimal cuts in lattices with random capacities. Examine rigorous bounds on geometric and energetic fluctuations of minimal surfaces, and understand the scaling relation that links these fluctuations. Learn about surface delocalization and localization in various dimensions, including power-law and sub-power-law fluctuations. Gain insights into new findings for one-dimensional cases, corresponding to non-integrable first-passage percolation. No prior knowledge of the topic is required to benefit from this comprehensive presentation, which includes joint work with Barbara Dembin, Dor Elboim, Daniel Hadas, Michal Bassan, and Shoni Gilboa.