Ergodic theorems in quantum probability: an application to the monotone stochastic processes

DOI10.2422/2036-2145.201506_009zbMath1388.60080arXiv1505.04688OpenAlexW1488651998MaRDI QIDQ4603994

Yun Gang Lu, Vitonofrio Crismale, Francesco Fidaleo

Publication date: 23 February 2018

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.04688

zbMATH Keywords

ergodic theoremsquantum probabilitymonotone stochastic processesYang-Baxter-Hecke quantisation

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Noncommutative dynamical systems (46L55) Ergodic theorems, spectral theory, Markov operators (37A30) Applications of functional analysis in quantum physics (46N50) States of selfadjoint operator algebras (46L30)

Related Items (12)

From discrete to continuous monotone C*-algebras via quantum central limit theorems ⋮ Limits of some weighted Cesaro averages ⋮ Tail algebras for monotone and \(q\)-deformed exchangeable stochastic processes ⋮ On truncated \(t\)-free Fock spaces: spectrum of position operators and shift-invariant states ⋮ Distributions for nonsymmetric monotone and weakly monotone position operators ⋮ Wick order, spreadability and exchangeability for monotone commutation relations ⋮ On the uniform convergence of ergodic averages for \(C^*\)-dynamical systems ⋮ Skew-product dynamical systems for crossed product \(C^\ast \)-algebras and their ergodic properties ⋮ Weakly monotone Fock space and monotone convolution of the Wigner law ⋮ Failure of the Ryll-Nardzewski theorem on the car algebra ⋮ Unique ergodicity and weakly monotone Fock space ⋮ On the monotone \(C^\ast \)-algebra

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