Speaker
Description
We combine resetting and first-passage to define "first-passage resetting”, where a random walk is reset to a fixed position due to a first-passage event of the walk itself. On the infinite half-line, first-passage resetting of isotropic diffusion is non-stationary, in which the number of resetting events grows with time as $t^{1/2}$. We calculate the resulting spatial probability distribution of the particle, and also obtain this distribution by a path decomposition approach. In a finite interval, we define an first-passage-resetting optimization problem that is motivated by reliability theory. Here, the goal is to operate a mechanical system close to its maximum capacity without experiencing too many breakdowns. When a breakdown occurs, the system is reset to its minimal operating point. We define and optimize an objective function that maximizes the reward (being close to maximum operation) minus a penalty for each breakdown. Finally, we study a first-passage-driven domain growth dynamics in which its boundary recedes by a specified amount when a diffusing particle reaches the boundary, after which resetting occurs. We find a wide range of dynamical behaviors for the domain growth rate in the interval and the semi-infinite line.
