Conditional means, vector pricings, amenability and fixed points in cones

2025/12/15 by Monod, Nicolas
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.13829

Abstract

We study 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 another. We characterize the groups for which these generalized probabilities can be stationary, respectively invariant. Our results deviate from the setting of classical probability; this leads to a new criterion for amenability and for fixed points in cones.

Citations

• Infinite stationary measures of co-compact group actions
• Fixed-points in the cone of traces on a C*-algebra
• Every exponential group supports a positive harmonic function
• Fixed points in convex cones
• Groups, Orders, and Dynamics

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• A Multidimensional Fatou Lemma for Conditional Expectations
• Unreal Probabilities: Partial Truth with Clifford Numbers
• Fixed points in convex cones
• A bang-bang principle for the conditional expectation vector measure