Pushforward Curve
A natural path connecting two probability measures in Wasserstein space, constructed by interpolating transport maps along a straight line to form a family of pushforward measures. It is used to define curve directions and Taylor expansions within the space of measures.
Timeline (last 90 days)
The method constructs quadratic models along push-forward curves, characterizing the curvature of energy in measure space using explicit self-adjoint second-order variational operators.
The push-forward curve is defined as ρ_t = ((1-t)id + tT)_#ρ, whose tangent vector at t=0 is T-id, corresponding to the displacement direction in Wasserstein space
All Facts (2)
The method constructs quadratic models along push-forward curves, characterizing the curvature of energy in measure space using explicit self-adjoint second-order variational operators.
50%UnverifiedThe push-forward curve is defined as ρ_t = ((1-t)id + tT)_#ρ, whose tangent vector at t=0 is T-id, corresponding to the displacement direction in Wasserstein space
50%