Ebook: Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Götze

​Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.

The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.

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Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.

The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich G?tze, a noted expert in this field.

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Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.

The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich G?tze, a noted expert in this field.

Content:
Front Matter....Pages i-viii
Front Matter....Pages 21-21
Distribution of Algebraic Numbers and Metric Theory of Diophantine Approximation....Pages 23-48
Fine-Scale Statistics for the Multidimensional Farey Sequence....Pages 49-57
Front Matter....Pages 59-59
On the Problem of Reversibility of the Entropy Power Inequality....Pages 61-74
On Probability Measures with Unbounded Angular Ratio....Pages 75-92
CLT for Stationary Normal Markov Chains via Generalized Coboundaries....Pages 93-112
Operator-Valued and Multivariate Free Berry-Esseen Theorems....Pages 113-140
A Characterization of Small and Large Time Limit Laws for Self-normalized L?vy Processes....Pages 141-169
Front Matter....Pages 171-171
A Nonparametric Theory of Statistics on Manifolds....Pages 173-205
Proportion of Gaps and Fluctuations of the Optimal Score in Random Sequence Comparison....Pages 207-233
Some Approximation Problems in Statistics and Probability....Pages 235-249
Front Matter....Pages 251-251
Moderate Deviations for the Determinant of Wigner Matrices....Pages 253-275
The Semicircle Law for Matrices with Dependent Entries....Pages 277-294
Limit Theorems for Random Matrices....Pages 295-317
A Conversation with Friedrich G?tze....Pages 1-20

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Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.

The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich G?tze, a noted expert in this field.

Content:
Front Matter....Pages i-viii
Front Matter....Pages 21-21
Distribution of Algebraic Numbers and Metric Theory of Diophantine Approximation....Pages 23-48
Fine-Scale Statistics for the Multidimensional Farey Sequence....Pages 49-57
Front Matter....Pages 59-59
On the Problem of Reversibility of the Entropy Power Inequality....Pages 61-74
On Probability Measures with Unbounded Angular Ratio....Pages 75-92
CLT for Stationary Normal Markov Chains via Generalized Coboundaries....Pages 93-112
Operator-Valued and Multivariate Free Berry-Esseen Theorems....Pages 113-140
A Characterization of Small and Large Time Limit Laws for Self-normalized L?vy Processes....Pages 141-169
Front Matter....Pages 171-171
A Nonparametric Theory of Statistics on Manifolds....Pages 173-205
Proportion of Gaps and Fluctuations of the Optimal Score in Random Sequence Comparison....Pages 207-233
Some Approximation Problems in Statistics and Probability....Pages 235-249
Front Matter....Pages 251-251
Moderate Deviations for the Determinant of Wigner Matrices....Pages 253-275
The Semicircle Law for Matrices with Dependent Entries....Pages 277-294
Limit Theorems for Random Matrices....Pages 295-317
A Conversation with Friedrich G?tze....Pages 1-20
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