44,522 research outputs found
Weil-Petersson perspectives
We highlight recent progresses in the study of the Weil-Petersson (WP)
geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on
and the understanding of infinite dimensional Teichm\"{u}ller spaces the reader
is directed to the recent work of Teo-Takhtajan. As part of the highlight, we
also present possible directions for future investigations.Comment: 18 page
Computability of probability measures and Martin-Lof randomness over metric spaces
In this paper we investigate algorithmic randomness on more general spaces
than the Cantor space, namely computable metric spaces. To do this, we first
develop a unified framework allowing computations with probability measures. We
show that any computable metric space with a computable probability measure is
isomorphic to the Cantor space in a computable and measure-theoretic sense. We
show that any computable metric space admits a universal uniform randomness
test (without further assumption).Comment: 29 page
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