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UID:www.tcs.tifr.res.in/event/181
DTSTAMP:20230914T125913Z
SUMMARY:Concentration of Measure in High Dimensions
DESCRIPTION:Speaker: Rakesh Venkat\nTata Institute of Fundamental Research\
 nSchool of Technology and Computer Science\nHomi Bhabha Road\n\nAbstract: 
 \nWe know that the Gaussian distribution concentrates sharply around its m
 ean\, ie. the probability mass outside a few standard deviations decreases
  exponentially in the number of steps taken. Such a concentration result c
 an actually be derived for areas and volumes in higher dimensions\, as pur
 ely geometrical facts. For instance\, for the unit sphere in n-dimensions\
 , most of the volume is concentrated around every slice through the equato
 r. Such results have various interesting implications. For example\, any L
 ipschitz function defined on the n-dimensional sphere is more or less cons
 tant! I will talk about some basic concentration of measure results\, and 
 related questions like isoperimetric inequalities\, the Brun-Minkowski ine
 quality and possibly something on metric embeddings\, depending on what ti
 me permits.\n
URL:https://www.tcs.tifr.res.in/web/events/181
DTSTART;VALUE=DATE:20110405
LOCATION:A-212 (STCS Seminar Room)
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