English

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

Probability 2026-01-12 v3 Dynamical Systems Functional Analysis Group Theory

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.

Keywords

Cite

@article{arxiv.2512.13829,
  title  = {Conditional means, vector pricings, amenability and fixed points in cones},
  author = {Nicolas Monod},
  journal= {arXiv preprint arXiv:2512.13829},
  year   = {2026}
}

Comments

v2: typos and fixed cross-ref numbering. v2: cosmetic changes only

R2 v1 2026-07-01T08:26:06.779Z