The Arboreal Gas - Percolative Properties of Random Forests

Explore the intriguing world of statistical mechanics in this 50-minute lecture presented by Tyler Helmuth from Durham University at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the concept of the arboreal gas, a probability measure derived from Bernoulli bond percolation conditioned on the event that the percolation subgraph is a forest. Discover how this model relates to the gelation of branched polymers and examine the percolative properties of random forests. Investigate current knowledge and conjectures surrounding the existence of giant trees within these structures. Gain insights into this fascinating area of research at the intersection of probability theory and statistical physics.