A stroll along the gamma [article]

Benjamin Arras, Yvik Swan
2016 arXiv   pre-print
We provide the first in-depth study of the "smart path" interpolation between an arbitrary probability measure and the gamma-(α, λ) distribution. We propose new explicit representation formulae for the ensuing process as well as a new notion of relative Fisher information with a gamma target distribution. We use these results to prove a differential and an integrated De Bruijn identity which hold under minimal conditions, hereby extending the classical formulae which follow from Bakry, Emery
more » ... Ledoux's Γ-calculus. Exploiting a specific representation of the "smart path", we obtain a new proof of the logarithmic Sobolev inequality for the gamma law with α≥ 1/2 as well as a new type of HSI inequality linking relative entropy, Stein discrepancy and standardized Fisher information for the gamma law with α≥ 1/2.
arXiv:1511.04923v3 fatcat:iayq3oaukva3leddnu4pwn4ck4