3 papers
math.AP2026
A gradient flow perspective on McKean-Vlasov equations in econophysics
David W. Cohen
We prove that the Gini coefficient of economic inequality is a Lyapunov functional for a class of nonlinear, nonlocal integro-differential equations arising at the intersection of…
math.AP2025
A Dynamical Equation for the Lorenz Curve: Dynamics of incomplete moments of probability distributions arising from Fokker-Planck equations
David W. Cohen, Merek Johnson, Bruce M. Boghosian
Fokker-Planck equations (forward Kolmogorov equations) evolve probability densities in time from an initial condition. For distributions over the real line, these evolution equatio…
math.AP2025
Variational principles on the space of Lorenz curves: Gradient structures and isometries inspired by Wasserstein geometry
David W. Cohen
We motivate and derive novel Riemannian gradient structures on the space of Lorenz curves, which preserve infinite-dimensional variational principles inherited from Fokker-Planck e…