Inspection Paradox Approach to Stochastic Resetting

Explore the intriguing concept of the inspection paradox and its application to stochastic resetting in this 46-minute lecture by Shlomi Reuveni at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the counter-intuitive phenomenon where passengers may wait longer than expected at bus stops, and discover how this principle extends to various random processes. Learn about diffusion, enzymatic reactions, stochastic search, and animal foraging through a series of central results derived using elementary mathematical tools. Gain deep probabilistic insights into stochastic resetting and its mechanisms, including the conditions under which it expedites process completion. Examine topics such as deterministic and Poisson-distributed bus arrivals, motion with constant velocity, diffusion with stochastic resetting, mean first passage time under restart, and the universality of fluctuations in optimal stochastic restart. Conclude with an exploration of experimental realizations and steady-state conditions in stochastic resetting systems.

Intro
Deterministic bus arrivals
Bus arrivals follow a Poisson process
General bus arrivals
Resolving the inspection paradox
Motion with constant velocity
Diffusion with stochastic resetting
Mean FPT under restart
Perturbative analysis
When does restart help?
Optimal stochastic restart renders fluctuations in FPT universal
Experimental realization of diffusion with resetting
Steady-state with stochastic resetting