# Dynamics of High Dimensional Complex Networks

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · New Jersey Institute of Technology (NJ) · $180,000

## Abstract

Stochastic ordinary differential equations on random graphs provide a general framework for modelling a range of important applications, including electrical power grids, communication or social networks, machine learning algorithms, epidemiology disease spread, neuroscience, and material models in statistical physics. This project will develop new characterizations of how interactions among large networks of individual particles or agents lead to important larger scale macroscopic phenomena. Examples range from the billions of neurons in the brain that can form macroscopic oscillations that are observable through electrocardiograms (ECG), to individual populations that may incur large outbreaks in disease spread.  The project will formulate new classes of macroscopic models that incorporate the microscopic effects of network delays, and local connectivity. It will also involve the training of graduate and undergraduate students in this research area.

This project aims to rigorously establish new macroscopic autonomous McKean-Vlasov equations (Fokker Planck type, hydrodynamic limits) for large systems of stochastically interacting particles on random graphs. A key mathematical contribution will be the introduction of new non-standard empirical measures that encode sufficient information regarding the microscopic state of the system. The structure of these measures are a key novelty that enables the derivation, and convergence to, autonomous McKean-Vlasov equations. The pro

## Key facts

- **NSF award ID:** 2511615
- **Awardee organization:** New Jersey Institute of Technology (NJ)
- **SAM.gov UEI:** SGBMHQ7VXNH5
- **PI:** James N MacLaurin
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $180,000
- **Funds obligated:** $180,000
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2511615

## Citation

> US National Science Foundation, Award 2511615, Dynamics of High Dimensional Complex Networks. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2511615. Licensed CC0.

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