scholarly journals Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution

Bernoulli ◽  
2021 ◽  
Vol 27 (1) ◽  
pp. 502-531
Author(s):  
Yuki Ueda
Keyword(s):  
Limit Theorems ◽  
Extreme Values ◽  
Convolution Semigroups ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution

scholarly journals New limit theorems related to free multiplicative convolution

2013 ◽  
Vol 214 (3) ◽  
pp. 251-264
Author(s):  
Noriyoshi Sakuma ◽  
Hiroaki Yoshida
Keyword(s):  
Limit Theorems ◽  
Multiplicative Convolution ◽  
Free Multiplicative Convolution

scholarly journals Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing

2005 ◽  
Vol 42 (3) ◽  
pp. 661-683 ◽  
Author(s):  
Larry Goldstein
Keyword(s):  
Fixed Points ◽  
Uniform Distribution ◽  
Central Limit ◽  
Limit Theorems ◽  
Extreme Values ◽  
Random Permutation ◽  
Central Limit Theorems ◽  
Finite Graphs ◽  
Size Bias ◽  
Pattern Occurrences

Berry-Esseen-type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are applied to the occurrences of fixed, relatively ordered subsequences (such as rising sequences) in a random permutation, and to the occurrences of patterns, extreme values, and subgraphs in finite graphs.

scholarly journals Limit theorems for generalized perimeters of random inscribed polygons. I

2020 ◽  
Vol 65 (4) ◽  
pp. 678-687
Author(s):  
Ekaterina N. Simarova ◽  
◽  
Keyword(s):  
Stochastic Geometry ◽  
Limit Theorems ◽  
Extreme Values ◽  
Limiting Behavior ◽  
Limit Distributions ◽  
Random Polygon ◽  
Generalized Perimeter ◽  
Definition Of ◽  
Inscribed Polygons

Lao and Mayer (2008) recently developed the theory of U-max-statistics, where instead of the usual averaging the values of the kernel over subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. Their limit distributions are related to distributions of extreme values. This is the first article devoted to the study of the generalized perimeter (the sum of side powers) of an inscribed random polygon, and of U-max-statistics associated with it. It describes the limiting behavior for the extreme values of the generalized perimeter. This problem has not been studied in the literature so far. One obtains some limit theorems in the case when the parameter y, arising in the definition of the generalized perimeter does not exceed 1.

scholarly journals Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing

2005 ◽  
Vol 42 (03) ◽  
pp. 661-683 ◽  
Author(s):  
Larry Goldstein
Keyword(s):  
Fixed Points ◽  
Uniform Distribution ◽  
Central Limit ◽  
Limit Theorems ◽  
Extreme Values ◽  
Random Permutation ◽  
Central Limit Theorems ◽  
Finite Graphs ◽  
Size Bias ◽  
Pattern Occurrences

Berry-Esseen-type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are applied to the occurrences of fixed, relatively ordered subsequences (such as rising sequences) in a random permutation, and to the occurrences of patterns, extreme values, and subgraphs in finite graphs.

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