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CATEGORIES:Probability
SUMMARY:Sumset bounds for the entropy on abelian groups -
Ioannis Kontoyiannis (Engineering\, Cambridge)
DTSTART;TZID=Europe/London:20190129T140000
DTEND;TZID=Europe/London:20190129T150000
UID:TALK114322AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/114322
DESCRIPTION:The development of the field of additive combinato
rics in recent years has provided\, among other th
ings\, a collection of fascinating and deep\, elem
entary tools for estimating the sizes of discrete
subsets of abelian groups. Tao in 2010 connected t
hese results with the entropy of discrete probabil
ity measures: Interpreting the entropy of a discre
te random variable as the logarithm of its "effect
ive support size\," he provided a series of new in
equalities for the discrete entropy. We will revie
w this background and describe how Tao's results e
xtend in a nontrivial way to the entropy of random
elements in general abelian groups. The somewhat
surprising key difference between the discrete and
the general case is that the "functional submodul
arity" property of the discrete entropy needs to b
e replaced by the general "data processing propert
y" of the entropy.\n\nNo background in information
theory\, entropy or additive combinatorics will b
e assumed.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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