  We address the issue of the dynamics of wealth accumulation and economic
crisis triggered by extreme inequality, attempting to stick to most possibly
intrinsic assumptions. Our general framework is that of pure or modified
multiplicative processes, basically geometric Brownian motions. In contrast
with the usual approach of injecting into such stochastic agent models either
specific, idiosyncratic internal nonlinear interaction patterns, or macroscopic
disruptive features, we propose a dynamic inequality model where the attainment
of a sizable fraction of the total wealth by very few agents induces a crisis
regime with strong intermittency, the explicit coupling between the richest and
the rest being a mere normalization mechanism, hence with minimal extrinsic
assumptions. The model thus harnesses the recognized lack of ergodicity of
geometric Brownian motions. It also provides a statistical intuition to the
consequences of Thomas Piketty's recent "$r>g$" (return rate $>$ growth rate)
paradigmatic analysis of very-long-term wealth trends. We suggest that the
"water-divide" of wealth flow may define effective classes, making an objective
entry point to calibrate the model. Consistently, we check that a tax mechanism
associated to a few percent relative bias on elementary daily transactions is
able to slow or stop the build-up of large wealth. When extreme fluctuations
are tamed down to a stationary regime with sizable but steadier inequalities,
it should still offer opportunities to study the dynamics of crisis and the
inner effective classes induced through external or internal factors.
