A uniform rate of convergence for the entropic potentials in the quadratic Euclidean setting

Puntos clave

• The aim is to establish the rate of uniform convergence for entropic potentials and their gradients to the Brenier potential and its gradient.
• Theoretical analysis of convergence rates in compact sets
• Investigation of entropic potentials and Brenier potential
• Use of convexity assumptions on measures
• Uniform convergence rates are bounded for entropic potentials in compact sets
• Gradients of entropic potentials also converge uniformly to those of the Brenier potential
• Results are valid under assumptions of absolute continuity and convexity