BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesca Zaffora Blando (Carnegie Mellon University) DTSTART:20221215T190000Z DTEND:20221215T200000Z DTSTAMP:20260423T035749Z UID:OLS/94 DESCRIPTION:Title: Ran domness and Invariance\nby Francesca Zaffora Blando (Carnegie Mellon U niversity) as part of Online logic seminar\n\n\nAbstract\nThe first (semi- )formal definition of randomness for infinite binary sequences dates back to von Mises’ work in the foundations of probability and statistics . According to von Mises\, a sequence is random if\, within it\, the relat ive frequencies of 0 and 1 converge to a limit and these limiting relative frequencies are invariant under a class of transformations called selecti on rules. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak and his account has been supplanted by the the ory of algorithmic randomness\, which characterizes randomness using the t ools of computability theory and measure theory. The goal of this talk is two-fold. First\, I will discuss a lesser-known characterization of Schnor r randomness due to Schnorr\, which demonstrates that it is possible to ob tain a satisfactory randomness notion by defining randomness\, analogously to how von Mises did it\, in terms of the invariance of limiting relative frequencies. Then\, I will discuss how other canonical algorithmic random ness notions are similarly characterizable in terms of the preservation of natural properties under the class of computable measure-preserving trans formations. This talk is based on joint work with Floris Persiau.\n LOCATION:https://researchseminars.org/talk/OLS/94/ END:VEVENT END:VCALENDAR