2016/08/18 by Thomas A. Courtade, Courtade, Thomas A.
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1608.05430
openalex publication_date 2016/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. As an application, we give a quantitative estimate of the deficit in the Gaussian logarithmic Sobolev inequality for radially symmetric functions.