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Physics Colloquium : "Rare events in interacting populations: from well-mixed to spatially-extended systems" | The Racah Institute of Physics

Physics Colloquium : "Rare events in interacting populations: from well-mixed to spatially-extended systems"

Date: 
Mon, 03/06/201912:00-13:30
Location: 
Levin building, Lecture Hall No. 8
Lecturer: Dr. Assaf Michael
Abstract:
Systems containing a discrete, large yet finite, population of interacting agents or dynamical units experience constant fluctuations, due to the discreteness of agents and the stochastic nature of the inter-agent interactions. Most of the time, such systems dwell in the vicinity of some attractor, undergoing small random excursions around it, while large fluctuations, on the order of the typical system size, are extremely rare. Yet, it is precisely these extreme, rare events, giving rise e.g. to population extinction, disease eradication, switching between cellular phenotypic states, the arrival of biomolecules at small cellular receptors, or power-grid desynchronization, which may be of key practical importance.
In most cases, systems of interacting agents are studied in a well-mixed framework, where each individual interacts with all others in the system. Yet, spatial degrees of freedom may have a nontrivial and even dramatic effect on the dynamics of such systems. In this talk I will discuss two prototypical examples of spatially-extended systems: a population residing on a complex network, with a nontrivial heterogeneous topology, and a fragmented meta-population residing on a network of patches, where the patches are coupled by diffusive migration. In particular, I will present analytical and numerical techniques that enable the accurate and efficient analysis of large deviations in such complex, many-body problems, and I will demonstrate that rare events are strongly influenced by the nontrivial spatial arrangement of individuals.