| Abstract: |
| Traditional analysis of stochastic systems often relies on pathwise trajectories within Euclidean space. However, a more profound understanding of complex phenomena, such as critical transitions, emerges when these systems are viewed as evolutions on a manifold of probability densities. This talk explores this geometric perspective on the Onsager Machlup most probable paths, Schrodinger bridges, and information geodesics. This provides a cohesive framework that links calculus of variations and information geometry, offering new insights into the most probable behaviours of uncertain systems. |
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