scholarly journals An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles

2016 ◽  
Author(s):  
Doron S. Lubinsky ◽  
Keyword(s):  
Correlation Functions ◽  
Universality Limits

DISCRETE CIRCULAR BETA ENSEMBLES

2013 ◽  
Vol 02 (03) ◽  
pp. 1350004
Author(s):  
D. S. LUBINSKY
Keyword(s):  
Probability Distribution ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Correlation Functions ◽  
Characteristic Polynomials ◽  
Normalization Constant ◽  
Discrete Measure ◽  
Universality Limits ◽  
Point Correlation ◽  
Beta Ensembles

Let μ be a measure with support on the unit circle and n ≥ 1, β > 0. The associated circular β ensemble involves a probability distribution of the form [Formula: see text] where C is a normalization constant, and [Formula: see text] We explicitly evaluate the m-point correlation functions when μ is replaced by a discrete measure on the unit circle, generated by paraorthogonal orthogonal polynomials associated with μ, and use this to investigate universality limits for sequences of such measures. We also consider ratios of products of random characteristic polynomials.

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

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