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SUMMARY:Andrew Mitchell (University of Birmingham)
DTSTART:20210218T153000Z
DTEND:20210218T164500Z
DTSTAMP:20260423T021408Z
UID:BODS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BODS/7/">Mea
 sure theoretic entropy of random substitutions</a>\nby Andrew Mitchell (Un
 iversity of Birmingham) as part of Bremen Online Dynamics Seminar\n\n\nAbs
 tract\nRandom substitutions and their associated subshifts provide\na mode
 l for structures that exhibit both long range order and positive\nentropy.
  In this talk we discuss the entropy of a large class of ergodic\nmeasures
 \, known as frequency measures\, that arise naturally from random\nsubstit
 utions.  We introduce a new measure of complexity\, namely measure\ntheore
 tic inflation word entropy\, and discuss its relationship to\nmeasure theo
 retic entropy.  We also show how this new measure of\ncomplexity can be us
 ed to provide a framework for the systematic study\nof the measure theoret
 ic entropy of random substitution subshifts.\n\nAs an application of our r
 esults\, we obtain closed form formulas for the\nentropy of a wide range o
 f random substitution subshifts and show that\nin many cases there exists 
 a frequency measure of maximal entropy.\nFurther\, for a class of random s
 ubstitution subshifts\, we show that this\nmeasure is the unique measure o
 f maximal entropy.\n\nThis is joint work with P. Gohlke\, R. Leek\, D. Rus
 t\, and T. Samuel.\n
LOCATION:https://researchseminars.org/talk/BODS/7/
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