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SUMMARY:Factors in probability and ergodic theory - Terry Soo (UCL)
DTSTART:20210126T140000Z
DTEND:20210126T150000Z
UID:TALK156397@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Sinai's factor theorem states that an ergodic stationary syste
 m of positive entropy has any independent and identically distributed (i.i
 .d.) system of no greater entropy as a factor.  In particular\, as a deter
 ministic function of a bi-infinite sequence of i.i.d. three-sided fair dic
 e 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 roll is shifted\, then its output under the function is g
 iven by shifting the original output.  We will discuss factor maps in prob
 ability and ergodic theory\, and recent work with Zemer Kosloff\, where we
  prove a version of Sinai's theorem where the input is given by independen
 t\, but not identical dice roll.
LOCATION:Zoom
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