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math.AP2026
Dimension-dependent symmetry breaking in a diffusive nonlocal interaction model
Dohyun Kim, Hansol Park, Woojoo Shim
We study the equilibrium structure and long-time behavior of a nonlinear Fokker--Planck equation with diffusion and nonlocal interactions generated by squared simplex volumes. For…
math.AP2026
Finite-dimensional reduction of a Wasserstein gradient flow and sharp decay rates
Dohyun Kim, Hansol Park, Woojoo Shim
We study the Wasserstein gradient flow generated by a family of extended generalized variance functionals, defined as the expected squared -dimensional volume of a simplex, whic…