A Gaussian convexity for logarithmic moment generating function

11/30/2023 4:00 pm - 5:00 pm
Benjamin McKenna Changji Xu Kevin Yang
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Probability Seminar

Speaker: Wei-Kuo Chen (University of Minnesota)

Title: A Gaussian convexity for logarithmic moment generating function

Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy.