Convex Hulls of Two Dimensional Stochastic Processes

Watch a detailed lecture by Professor Satya Majumdar from Université Paris Saclay exploring the statistical properties of convex hulls in two-dimensional stochastic processes. Discover how Cauchy's formula can be adapted to random curves, enabling explicit calculations of mean perimeter and area for convex hulls of arbitrary two-dimensional stochastic processes. Learn about practical applications through specific examples, including independent planar Brownian paths for estimating animal population home ranges and planar branching Brownian motion with death for modeling animal epidemic outbreaks. Examine additional case studies featuring active run-and-tumble processes and resetting Brownian motion, providing a comprehensive understanding of random geometry and extreme value statistics in two-dimensional space.