Researcher(s)
- Max Santos, Actuarial Sciences, University of Delaware
- Ryan Eustace, Statistics, University of Delaware
Faculty Mentor(s)
- Mokshay Madiman, Mathematical Sciences, University of Delaware
Abstract
This project investigates the Gaussian Free Field (GFF), a fundamental model in probability and statistical mechanics. As a team, we investigated the behavior of the GFF over discrete lattices with a focus on the distribution of its marginals. We also explored the structural properties governing these distributions, specifically analyzing their connections to the Fortuin-Kasteleyn-Ginibre (FKG) inequality, log-supermodularity, and log-concavity. These properties clarify marginal distribution and the correlation of neighboring nodes in the GFF. Finally, we built and ran simulations to visualize the GFF and gain a better understanding of the associated Green’s function and how it reflects the covariance of the GFF.