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Soft Seminars
Group avoidance through collective resetting
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Europe/Stockholm
Albano Building 3
Albano Building 3
Description
Stochastic resetting is well understood for single particles, but many problems involve groups whose resetting rule is set by the group itself. In computational science, for example, swarm-search algorithms deploy many walkers that periodically relocate to the fittest searcher. In artificial selection, repeatedly choosing the subpopulation farthest from an undesired state, such as antibiotic resistance, could keep a microbial population away from that state. Inspired by these examples, we study diffusing particles in a confining potential that all reset at a constant rate to the position of the most extreme particle.
Treating the group’s center of mass as an effective particle, we use renewal theory and extreme-value statistics to build a general framework for group resetting. The framework yields analytical stationary results that agree with many-particle simulations. We apply it to the problem of avoiding an undesired region located at the center of the attracting potential, so that the particles constantly drift toward it and only resetting can hold them away. We then add an absorbing boundary to study first-passage dynamics. Resetting produces hitting-time distributions with plateaus spanning several orders of magnitude, and the mean and most probable arrival times become widely separated. The system therefore lacks a single characteristic time scale. This shows that controlling collective resetting requires looking beyond the average.