[Todos] Recordatorio: Seminario de Probabilidad Mañana

[Matthieu Jonckheere]

PROXIMO ENCUENTRO: Miércoles 8 de Mayo, 12:00hs.

>
> EXPOSITOR: Quinn Culver, University of  Notre Dame.
>
> TITULO: Algorithmically Random Measures
>
> LUGAR: Departamento de Matemática, Aula de seminarios, 2do piso, Pabellón
> 1.
>
> RESUMEN: *
>
> Algorithmic randomness attempts to answer the question "What exactly is a
> random real number?" It does so by declaring that a real is nonrandom if it
> can be captured in a null set that can be effectively (aka computably)
> approximated from without by open sets. There is a rich interplay between
> the theory of algorithmic randomness, the theory of computation (Turing
> degrees), and probability theory. Recently, the theory of algorithmic
> randomness with respect to other (i.e. non-uniform) measures has been
> developed. This development, coupled with the fact that the space of
> probability measures on the unit interval a nice enough space on which to
> do computability, motivates the questions "Is there a natural measure on
> the space of measures? What do its algorithmically random elements look
> like?"
> *
> *
> In attempt to answer these questions, we define a natural, computable map
> that associates to each real a Borel probability measure, so that we can
> talk about algorithmically random measures. We show that such random
> measures are atomless and mutually singular with respect to Lebesgue. We
> introduce a certain information-theoretic-ish property that lies strictly
> between atomlessness and absolute continuity (with respect to the Lebesgue
> measure) that we conjecture random measures satisfy. We then discuss other
> maps, ask the question "Why is the first map more natural?", and discuss
> some ways in which that question might be precisifiable.*
>
>
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