Spectral monotonicity under Gaussian convolution
Bo’az Klartag, Eli Putterman
Abstract
We show that the Poincaré constant of a log-concave measure in Euclidean space is monotone increasing along the heat flow. In fact, the entire spectrum of the associated Laplace operator is monotone decreasing. Two proofs of these results are given. The first proof analyzes a curvature term of a certain time-dependent diffusion, and the second proof constructs a contracting transport map following the approach of Kim and Milman.
Topics & Concepts
Monotonic functionConvolution (computer science)GaussianMathematicsStatistical physicsApplied mathematicsComputer scienceMathematical analysisPhysicsArtificial intelligenceArtificial neural networkQuantum mechanicsPoint processes and geometric inequalitiesNumerical methods in inverse problemsGeometric Analysis and Curvature Flows