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SUMMARY:Tales of Random Projections - Kavita Ramanan (Brown University)
DTSTART;VALUE=DATE-TIME:20190528T110000Z
DTEND;VALUE=DATE-TIME:20190528T120000Z
UID:https://talks.ox.ac.uk/talks/id/0cb9b171-07b2-434d-8f2e-eea8bff47784/
DESCRIPTION:The interplay between geometry and probability in high-dimensi
onal spaces is an active subject of current research. Classical theorems i
n probability theory such as the central limit theorem and Cramerâ€™s theo
rem can be viewed as providing information about certain scalar projection
s of high-dimensional product measures. In this talk we will describe th
e behavior of random projections of more general (possibly non-product) hi
gh-dimensional measures\, which are of interest in diverse fields\, rangin
g from asymptotic convex geometry to high-dimensional statistics. Althou
gh the study of (typical) projections of high-dimensional measures dates b
ack to Borel\, only recently has a theory begun to emerge\, which in parti
cular identifies the role of certain geometric assumptions that lead to be
tter behaved projections. A particular question of interest is to identi
fy what properties of the high-dimensional measure are captured by its lo
wer-dimensional projections. While fluctuations of these projections hav
e been studied over the past decade\, we describe more recent work on the
tail behavior of multidimensional projections\, and associated conditional
limit theorems. This is based on joint work with Steven Soojin Kim and
Nina Gantert.\nSpeakers:\nKavita Ramanan (Brown University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/0cb9b171-07b2-434d-8f2e-eea8bff47784/
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DESCRIPTION:Talk:Tales of Random Projections - Kavita Ramanan (Brown Unive
rsity)
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