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CATEGORIES:Probability
SUMMARY:Factors in probability and ergodic theory - Terry
Soo (UCL)
DTSTART;TZID=Europe/London:20210126T140000
DTEND;TZID=Europe/London:20210126T150000
UID:TALK156397AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/156397
DESCRIPTION:Sinai's factor theorem states that an ergodic stat
ionary system of positive entropy has any independ
ent and identically distributed (i.i.d.) system of
no greater entropy as a factor. In particular\,
as a deterministic function of a bi-infinite seque
nce of i.i.d. three-sided fair dice roll\, we can
produce a bi-infinite sequence of i.i.d. fair coin
flips\; furthermore\, the deterministic function
is equivariant\, so that if the sequence of dice r
oll is shifted\, then its output under the functio
n is given by shifting the original output. We wi
ll discuss factor maps in probability and ergodic
theory\, and recent work with Zemer Kosloff\, wher
e we prove a version of Sinai's theorem where the
input is given by independent\, but not identical
dice roll.
LOCATION:Zoom
CONTACT:Perla Sousi
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