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Emergent Behavior in Collective DynamicsMathematical Physics & Probability
A fascinating aspect of collective dynamics is the self-organization of small-scales and their emergence as higher-order patterns -- clusters, flocks, tissues, parties.
The emergence of different patterns can be described in terms of few fundamental “rules of interactions”. I will discuss recent results of the large-time, large-crowd dynamics, driven by anticipation that tend to align the crowd, while other pairwise interactions keep the crowd together while preventing over-crowding.
In particular, I address the question how short-range interactions lead to the emergence of long-range patterns, comparing different rules of interactions based on geometric vs. topological neighborhoods.