This talk will present a joint work 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 talk about an extension of first-passage resetting into
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., R.-F., J., Redner, S. (2020). Phys. Rev. Letters, 125(5), 050602;
de Bruyne, B., R.-F., J., Redner, S. (2021). J. Stat. Mech., 2021(10), 103405;