Probabilistic stable functions on discrete cones are power series
Raphaëlle Crubillé
IMDEA Software Institute, Madrid
http://research.crubille.lautre.net/
Date(s) : 25/04/2019 iCal
11h00 - 12h30
The category of probabilistic coherence spaces (PCoh_!), introduced by Danos and Ehrhard, is a fully abstract model for PCF with *discrete* probabilities, where morphisms can be seen as power series. The category Cstab_m, of measurable cones and measurable stable functions, has been introduced by Ehrhard, Pagani and Tasson as a model for PCF with *continuous* probabilities.
In this talk, we will study the shape of stable functions when they are between discretecones: we will show that they can actually be seen as generalized power series. The proof is based on a generalization of a theorem from real analysis due to Bernstein, that states that all absolutely monotonous functions on reals are power series. From there, we will build a full and faithful functor from PCoh_! into Cstab_m that moreover preserves the cartesian closed structure.
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