2022/09/06 by Vitonofrio Crismale, Stefano Rossi, Crismale, Vitonofrio +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Quantum Mechanics and Applications #Random Matrices and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2209.02325
openalex publication_date 2022/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spreadability of a sequence of random variables is a distributional symmetry that is implemented by suitable actions of \mathbbJ_ℤ, the unital semigroup of strictly increasing maps on ℤ with cofinite range. We show that \mathbbJ_ℤ is left amenable but not right amenable, although it does admit a right Folner sequence. This enables us to prove that on the CAR algebra \rm CAR(ℤ) there exist spreadable states that fail to be exchangeable. Moreover, we also show that on \rm CAR(ℤ)there exist stationary states that fail to be spreadable.