BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew Mitchell (University of Birmingham) DTSTART:20210413T123000Z DTEND:20210413T133000Z DTSTAMP:20260423T021448Z UID:OWNS/40 DESCRIPTION:Title: Me asure theoretic entropy of random substitutions\nby Andrew Mitchell (U niversity of Birmingham) as part of One World Numeration seminar\n\n\nAbst ract\nRandom substitutions and their associated subshifts provide a model for structures that exhibit both long range order and positive topological entropy. In this talk we discuss the entropy of a large class of ergodic measures\, known as frequency measures\, that arise naturally from random substitutions. We introduce a new measure of complexity\, namely measure t heoretic inflation word entropy\, and discuss its relationship to measure theoretic entropy. This new measure of complexity provides a framework for the systematic study of measure theoretic entropy for random substitution subshifts. \n\nAs an application of our results\, we obtain closed form f ormulas for the entropy of frequency measures for a wide range of random s ubstitution subshifts and show that in many cases there exists a frequency measure of maximal entropy. Further\, for a class of random substitution subshifts\, we show that this measure is the unique measure of maximal ent ropy.\n\nThis talk is based on joint work with P. Gohlke\, D. Rust\, and T . Samuel.\n LOCATION:https://researchseminars.org/talk/OWNS/40/ END:VEVENT END:VCALENDAR