Simple wealth distribution model causing inequality-induced crisis without external shocks

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.Comment: 15 pages, 11 figures. Work initiated from discussion on Aristotle's status revisited by Paul Jorion in the many cases where the law of supply and demand fails. Accepted for publication in Physical Review E on April 19, 201

Milky Way and Andromeda past-encounters in different gravity models: the impact on the estimated Local Group mass

The Two-body problem of $M31$ and the Milky Way (MW) galaxies with a Cosmological Constant background is studied, with emphasis on the possibility that they experienced Past Encounters. By implementing the Timing Argument (TA), it is shown that if $M{31}$ and the MW have had more than one encounter then the deduced mass of the Local Group (LG) would be larger. Past encounters are possible only for non-zero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. Using a recent $Gaia$ - based measurement of the transverse velocity we show that the presence of the Cosmological Constant requires the mass for the LG to be $35\%$ higher: $3.36^{+1.14}_{-0.70} \cdot 10^{12} M_{\odot}$ with no Cosmological Constant or $4.54^{+1.20}_{-0.75} \cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. If the LG has had one past encounter, the LG mass is $9.99^{+2.22}_{-1.58}\cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. Modified Newtonian Dynamics (MOND) is studied as the accelerations of the Local Group are fully in the deep-MOND regime. MOND yields the order of magnitude for the expected baryonic mass only if at least one encounter occurred. While we only consider the LG as two point masses, our calculations provide a benchmark for future work with simulations to test Dynamical Friction and other effects. This model can be also used to test screening mechanisms and alternative theories of gravity.Comment: 16 pages. A revised versio