Entropy Jumps for Radially Symmetric Random Vectors

Understand

We establish a quantitative bound on the entropy jump associated to the sum of independent, identically distributed (IID) radially symmetric random vectors having dimension greater than one.

• Following the usual approach, we first consider the analogous problem of Fisher information dissipation, and then integrate along the Ornstein-Uhlenbeck semigroup to obtain an entropic inequality.
• In a departure from previous work, we appeal to a result by Desvillettes and Villani on entropy production associated to the Landau equation.
• This obviates strong regularity assumptions, such as presence of a spectral gap and log-concavity of densities, but comes at the expense of radial symmetry.