Role of volatility mixing in wealth condensation transition

TL;DR

This paper investigates how heterogeneous volatility in networked wealth models influences wealth condensation, revealing that volatility mixing can lower the tail exponent and induce a transition to wealth concentration.

Contribution

It extends the Bouchaud--M{é}zard model by incorporating binary volatility and analyzes how volatility configuration affects wealth distribution and condensation.

Findings

Volatility mixing lowers the effective tail exponent of wealth distribution.

Local interactions between different volatility groups neutralize group-wise exponents.

Volatility heterogeneity can trigger wealth condensation across a critical threshold.

Abstract

We study the role of heterogeneous volatility in a networked wealth dynamics model and its impact on the wealth condensation transition. Extending the Bouchaud--M{\'e}zard framework, we introduce binary volatility in networks and investigate how its configuration affects the effective power-law tail exponent of the wealth distribution. Using a stochastic block model, we control the mixing between volatility groups and show that the effective exponent is governed not only by the global parameter $\Lambda=2J/\beta^2$ but also by the volatility configuration in the network. We find that local interactions between nodes with different volatility induce a neutralization of group-wise exponents, which lowers the aggregate tail exponent and can drive a condensation transition across $\gamma_{\rm c}=2$. Our results identify volatility mixing as another control mechanism for wealth condensation and highlight the importance of noise heterogeneity in nonequilibrium systems on networks.