Stochastic Search Processes and Encounter-Based Models of Absorption

Explore a 59-minute research seminar delivered by Professor Paul Bressloff from Imperial College London focusing on encounter-based methods for modeling absorption processes in mathematical biology. Delve into the probabilistic framework for analyzing absorption events on target surfaces or interiors, where absorption occurs when contact time exceeds a random threshold. Learn about Markovian and non-Markovian absorption scenarios, examining how exponential and non-exponential probability distributions affect the process. Discover the application of Brownian functionals like occupation time and boundary local time in partially absorbing targets, and understand how the theory extends to active run-and-tumble particles. Examine practical applications in diffusion through semi-permeable membranes, connecting theoretical frameworks to real-world biological systems.