BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/1261
DTSTAMP:20230914T125956Z
SUMMARY:Convex influences and a quantitative Gaussian correlation inequalit
y
DESCRIPTION:Speaker: Anindya De (University of Pennsylvania)\n\nAbstract: \
nThe Gaussian correlation inequality (GCI)\, proven by Royen in 2014\, st
ates that any two centrally symmetric convex sets (say K and L) in the Gau
ssian space are positively correlated. We will prove a new quantitative ve
rsion of the GCI which gives a lower bound on this correlation based on th
e "common influential directions" of K and L. This can be seen as a Gaussi
an space analogue of Talagrand's well known correlation inequality for mon
otone functions. To obtain this inequality\, we propose a new approach\, b
ased on analysis of Littlewood type polynomials\, which gives a recipe to
transfer qualitative correlation inequalities into quantitative correlatio
n inequalities. En route\, we also give a new notion of influences for con
vex symmetric sets over the Gaussian space which has many of the propertie
s of influences from Boolean functions over the discrete cube. Much remain
s to be explored\, in particular\, about this new notion of influences for
convex sets.\n\nBased on joint work with Shivam Nadimpalli and Rocco Serv
edio.\n
URL:https://www.tcs.tifr.res.in/web/events/1261
DTSTART;TZID=Asia/Kolkata:20221227T160000
DTEND;TZID=Asia/Kolkata:20221227T170000
LOCATION:A201
END:VEVENT
END:VCALENDAR