Reducing high dimensional systems to low dimensions
Abstract: In this joint work
with Matteo Tanzi and Tiago Pereira, we study high dimensional networks of
heterogeneously coupled maps. Using transfer operators on invariant cones of
densities and a concentration inequality, we show rigorously that different
types of dynamics emerge across distinct connectivity layers. Moreover, it
turns out that data arising from such systems can be used to reconstruct
detailed information on the dynamics and the network.