Speaker
Description
Understanding macroscopic phenomena in complex systems requires accurate modeling of stochastic dynamics in structured interactions. We present a computational framework based on dynamic cavity equations for stochastic processes on sparse networks. Using a second-order small-coupling expansion, we approximate cavity marginals as Gaussian. For linear dynamics with additive noise, this yields a closed set of causal integro-differential equations for cavity versions of one-time and two-time averages, providing an exact description within the local tree-like approximation and retrieving classical results for sparse random matrices. Nonlinear forces, global constraints, and state-dependent noise are addressed via a self-consistent perturbative closure. Our approach extends dynamical mean-field methods beyond fully connected models, enabling the study of nonlinearity and heterogeneity in realistic networks.
We illustrate this with (i) the Bouchaud-Mézard model for wealth distribution, where multiplicative noise drives wealth condensation, and our method captures the transition to the wealth-condensed phase in sparse networks; and (ii) the random Generalized Lotka-Volterra model, an ecological system where interaction heterogeneity affects species coexistence and stability. Despite their differences, both models exhibit nonlinear stochastic interactions on sparse networks, which our method correctly captures.
This highlights the framework’s versatility in addressing complex systems from economic markets to ecological communities. Beyond these cases, our approach provides a powerful tool to study stochastic systems on sparse networks in diverse contexts, such as financial networks, learning dynamics in artificial intelligence, and adaptive systems in evolutionary biology.
| Role | Master/PhD student |
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