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math.PR2025
Conditional means, vector pricings, amenability and fixed points in cones
Nicolas Monod
We develop a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to anoth…
math.FA2025
Eigenfunctionals for positive operators
Nicolas Monod
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators…
math.GR2025
A fixed-point theorem for face maps, or deletion-tolerant random finite sets
Tom Hutchcroft, Nicolas Monod, Omer Tamuz
We establish a fixed-point theorem for the face maps that consist in deleting the th entry of an ordered set. Furthermore, we show that there exists random finite sets of intege…