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SUMMARY:Ergodic theory and strong randomness notions - Franklin\, J (Unive
 rsity of Connecticut)
DTSTART:20120705T133000Z
DTEND:20120705T140000Z
UID:TALK38868@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:There has been a great deal of interest recently in the connec
 tion between\nalgorithmic randomness and ergodic theory\, which naturally 
 leads to the\nquestion of how much one can say if the transformations in q
 uestion need\nnot be ergodic. We have essentially reversed a result of V'y
 ugin and shown\nthat if an element of the Cantor space is not Martin-L&oum
 l\;f random\, then\nthere is a computable function and a computable transf
 ormation for which\nthis element is not typical with respect to the ergodi
 c theorem. More\nrecently\, we have shown that every weakly 2-random eleme
 nt of the Cantor\nspace is typical with respect to the ergodic theorem for
  every lower\nsemicomputable function and computable transformation. I wil
 l explain\nthe proof of the latter result and discuss the technical diffic
 ulties\npresent in producing a full characterization.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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