First-passage resetting

In this talk I will present results obtained recently with B. de Bruyne and S. Redner on first-passage resetting, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain, we calculate the resulting spatial probability distribution of the particle analytically, and also obtain this distribution by a path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting: a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset-trigger point. This scenario is motivated by reliability theory. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.
Time permitting, I will also show other extensions of first-passage resetting, in particular a minimalist dynamical model of wealth evolution and wealth sharing among $N$ agents as a platform to compare the relative merits of altruism and individualism.
References
de Bruyne, B., Randon-Furling, J., Redner, S. (2020). Optimization in first-passage resetting. Physical Review Letters, 125(5), 050602.
de Bruyne, B., Randon-Furling, J., Redner, S. (2021). A tale of two (and more) altruists. Journal of Statistical Mechanics: Theory and Experiment, 2021(10), 103405.