Lecturer: Prof. Sid Redner, Santa Fe Institute
 Abstract:
We investigate classic diffusion with the added feature that a diffusing
particle is reset to its starting point each time the particle reaches a
specified threshold. In an infinite domain, first-passage resetting is
non-stationary and its probability distribution exhibits rich features.
In a finite domain, first-passage resetting leads to a nontrivial
optimization in which a cost is incurred whenever the particle is reset
and a reward is given when the particle stays near the reset (maximal
performance) point. We derive the condition to optimize the net gain
(reward-cost). We also explore simple consequences of first-passage
resetting in a toy model of wealth sharing.