Bouchaud-Mézard Model
The Bouchaud-Mézard model is a cornerstone of econophysics. It describes how wealth is accumulated and redistributed in a population of agents interacting on a exchange network.
The evolution of wealth $x_i$ of agent $i$ follows the following coupled SDE: $$dx_i(t) = J \sum_{j \in \partial i} (x_j(t) - x_i(t)) dt + \sigma x_i(t) d\eta_i(t),$$ where $J \sum_{j \in \partial i} (x_j(t) - x_i(t))$ represents the exchange of wealth with neighboring agents, while $\sigma x_i(t) d\eta_i(t)$ represents the change of wealth due to investment in the stock-market. We defined $\partial i$ as the neighborood of agent $i$.
In this page you can test the model in real time. The widget shows the stationary distribution of normalized wealths. The computations are exectued by a FastAPI backend on Hugging Face Spaces.
Interactive Simulator
Technical Notes
The numerical integration uses the Milstein scheme. If the simulation does not start immediatelly, the server hosting the code could be “awakening”: please try to run it again after few minutes.
Mattia Tarabolo
Researcher in Statistical Physics
My research interests include statistical physics, neural networks and biological systems.