
СЕМИНАРЫ 
Городской семинар по теории вероятностей и математической статистике



Firstpassage resetting Julien RandonFurling^{} 

Аннотация: In this talk I will present results obtained recently with B. de Bruyne and S. Redner on firstpassage resetting, where the resetting of a random walk to a fixed position is triggered by a firstpassage 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 firstpassage resetting: a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the resettrigger 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 firstpassage resetting, in particular a minimalist dynamical model of wealth evolution and wealth sharing among References de Bruyne, B., RandonFurling, J., Redner, S. (2020). Optimization in firstpassage resetting. Physical Review Letters, 125(5), 050602. de Bruyne, B., RandonFurling, J., Redner, S. (2021). A tale of two (and more) altruists. Journal of Statistical Mechanics: Theory and Experiment, 2021(10), 103405. Язык доклада: английский 