Role of volatility mixing in wealth condensation transition

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.