Large Scale Dynamics and Geometry in Stochastic Systems
Abstract
Major Goals: Major goals of the grant are to understand `scales' in stochastic systems and connections to geometry. Interacting particle systems as spatially discrete models of physical and other phenomena are studied. Also, stochastic networks, and flows of Markov chains are to be investigated. Problems include understanding large scale features as a consequence of types of microscopic interactions. Such an understanding allows to classify behaviors in complex systems at a `high' level, yielding a description in reduced variables, depending on the type of `street' level dynamics. In this context, the main aim is to identify universal behaviors and provide a detailed understanding of the scaling limits in different settings which, although fundamental, have been difficult to analyze as they involve nonlinear, singular, or heterogeneous components incorporating geometry. To this end, a departure from previous methods and a common theme of the work is to develop new robust mathematical methods for `local' homogenizations which take account of both the stochastic particle interactions and the complex structure of the underlying graphs. As such, we hope to address a host of previously intractable problems including capturing `interface flow', `flows through traps', and `non-Gaussian effects in fluctuations'. These limits are anticipated to connect integrally with notions in geometry, statistics, and analysis.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 07, 2022
- Accession Number
- AD1201052
Entities
People
- Sunder Sethuraman
Organizations
- University of Arizona