scholarly journals DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY

2006 ◽  
Vol 09 (01) ◽  
pp. 77-106 ◽  
Author(s):  
ROMUALD LENCZEWSKI ◽  
RAFAŁ SAŁAPATA
Keyword(s):  
Explicit Formula ◽  
Free Product ◽  
Central Limit ◽  
Limit Theorems ◽  
Free Probability ◽  
Explicit Formulas ◽  
Cauchy Transforms ◽  
New Type ◽  
Monotone Probability

We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki in monotone probability and the free product of states of Avitzour and Voiculescu in free probability. We derive the associated basic limit theorems and develop the combinatorics based on non-crossing ordered partitions with monotone order starting from depth m. We deduce an explicit formula for the Cauchy transforms of the m-monotone central limit measures and for the associated Jacobi coefficients. A new type of combinatorics of inner blocks in non-crossing partitions leads to explicit formulas for the mixed moments of m-monotone Gaussian operators, which are new even in the case of monotone independent Gaussian operators with arcsine distributions.

Linear de-preferential urn models

2018 ◽  
Vol 50 (4) ◽  
pp. 1176-1192 ◽  
Author(s):  
Antar Bandyopadhyay ◽  
Gursharn Kaur
Keyword(s):  
Weight Function ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Urn Models ◽  
Doubly Stochastic ◽  
New Type ◽  
Urn Scheme ◽  
Selection Probabilities ◽  
Random Configuration

Abstract In this paper we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the de-preferential urn scheme. We establish the almost-sure limit of the random configuration for any balanced replacement matrix R. In particular, we show that the limiting configuration is uniform on the set of colours if and only if R is a doubly stochastic matrix. We further establish the almost-sure limit of the vector of colour counts and prove central limit theorems for the random configuration as well as for the colour counts.

Λ-FREE PROBABILITY

2004 ◽  
Vol 07 (01) ◽  
pp. 27-41 ◽  
Author(s):  
WOJCIECH MŁOTKOWSKI
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Free Product ◽  
Central Limit ◽  
Free Probability ◽  
Noncommutative Probability

We introduce and study a notion of Λ-freeness, which generalises both freeness and independence in the context of noncommutative probability. In particular, we extend Voiculescu's construction of the free product of representations of unital *-algebras. A central limit theorem is also proved.

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
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