scholarly journals From discrete to continuous monotone C*-algebras via quantum central limit theorems

2017 ◽  
Vol 20 (02) ◽  
pp. 1750013 ◽  
Author(s):  
Vitonofrio Crismale ◽  
Francesco Fidaleo ◽  
Yun Gang Lu
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Fock Spaces ◽  
Test Functions ◽  
Creation And Annihilation Operators ◽  
C Algebras ◽  
Joint Distributions ◽  
Monotone Formula ◽  
Weighted Sequences

We prove that all finite joint distributions of creation and annihilation operators in monotone and anti-monotone Fock spaces can be realised as Quantum Central Limit of certain operators in a [Formula: see text]-algebra, at least when the test functions are Riemann integrable. Namely, the approximation is given by weighted sequences of creators and annihilators in discrete monotone [Formula: see text]-algebras, the weights being related to the above cited test functions.

scholarly journals CONSTRUCTIVE UNIVERSAL CENTRAL LIMIT THEOREMS BASED ON INTERACTING FOCK SPACES

2005 ◽  
Vol 08 (04) ◽  
pp. 631-650 ◽  
Author(s):  
L. ACCARDI ◽  
V. CRISMALE ◽  
Y. G. LU
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Probability Measure ◽  
Central Limit ◽  
Limit Theorems ◽  
Fock Space ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Fock Spaces ◽  
Interacting Fock Space

Cabana-Duvillard and lonescu11 have proved that any symmetric probability measure with moments of any order can be obtained as central limit theorem of self-adjoint, weakly independent and symmetrically distributed (in a quantum souse) random variables. Results of this type will be called "universal central limit theorem". Using Interacting Fock Space (IFS) techniques we extend this result in two directions: (i) we prove that the random variables can be taken to be generalized Gaussian in the sense of Accardi and Bożejko3 and we give a realization of such random variables as sums of creation, annihilation and preservation operators acting on an appropriate IFS; (ii) we extend the above-mentioned result to the nonsymmetric case. The nontrivial difference between the symmetric and the nonsymmetric case is explained at the end of the introduction below.

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

scholarly journals Central limit theorems for supercritical superprocesses

2015 ◽  
Vol 125 (2) ◽  
pp. 428-457 ◽  
Author(s):  
Yan-Xia Ren ◽  
Renming Song ◽  
Rui Zhang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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