A Some useful probabilistic inequalities

1996 ◽  
pp. 241-244
Keyword(s):  
Probabilistic Inequalities

Probabilistic inequalities for evaluating structural network measures

2014 ◽  
Vol 288 ◽  
pp. 220-245 ◽  
Author(s):  
Veronika Kraus ◽  
Matthias Dehmer ◽  
Frank Emmert-Streib
Keyword(s):  
Network Measures ◽  
Structural Network ◽  
Probabilistic Inequalities

A System of Probabilistic Inequalities

SIAM Review ◽  
1983 ◽  
Vol 25 (4) ◽  
pp. 569-570
Author(s):  
T. ten Raa
Keyword(s):  
Probabilistic Inequalities

scholarly journals A Combinatorial Approach to Small Ball Inequalities for Sums and Differences

2018 ◽  
Vol 28 (1) ◽  
pp. 100-129 ◽  
Author(s):  
JIANGE LI ◽  
MOKSHAY MADIMAN
Keyword(s):  
Hilbert Spaces ◽  
Vector Spaces ◽  
Combinatorial Approach ◽  
Kissing Number ◽  
Small Ball ◽  
Small Ball Probabilities ◽  
Packing Problems ◽  
Number Problem ◽  
Probabilistic Inequalities ◽  
Independent Identically Distributed

Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent, identically distributed random elements taking values in very general sets. Depending on the setting – abelian or non-abelian groups, or vector spaces, or Banach spaces – we provide a collection of inequalities relating different small ball probabilities that are sharp in many cases of interest. We prove these distribution-free probabilistic inequalities by showing that underlying them are inequalities of extremal combinatorial nature, related among other things to classical packing problems such as the kissing number problem. Applications are given to moment inequalities.

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