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SUMMARY:De Bruijn's identity and stability in the Entropy Power Inequality
  without finite variance - Dr Lampros Gavalakis\, DPMMS\, University of Ca
 mbridge
DTSTART:20251022T130000Z
DTEND:20251022T140000Z
UID:TALK239449@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:De Bruijn's identity is a celebrated result in information the
 ory\, linking the derivative of entropy with respect to the variance of Ga
 ussian perturbation to the Fisher information. While it has been widely ap
 plied and rigorously derived under second moment or mild regularity assump
 tions\, the necessary conditions ensuring the validity of the required exc
 hanges of differentiation and integration have not been fully identified i
 n the literature.\n\nIn this talk\, we present necessary and sufficient co
 nditions for de Bruijn's identity\, as well as for continuity of entropy w
 ith respect to Gaussian perturbation. We explain their implications for ch
 aracterizing the equality case in the Entropy Power Inequality (EPI) under
  minimal assumptions. We then turn to the question of stability in the EPI
 . After reviewing some existing negative and positive results\, we conclud
 e with a qualitative stability theorem in the weak convergence sense\, val
 id under very mild assumptions.\n\nThe talk is based on joint work with Io
 annis Kontoyiannis (Cambridge). 
LOCATION:MR5\, CMS Pavilion A
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