Format:
Online-Ressource (VIII, 317 p. 2 illus., 1 illus. in color, digital)
ISBN:
9783642360688
Series Statement:
Springer Proceedings in Mathematics & Statistics 42
Content:
W. van Zwet: A conversation with Friedrich Götze -- V. Bernik, V. Beresnevich, F. Götze, O. Kukso: Distribution of algebraic numbers and metric theory of Diophantine approximation -- J. Marklof: Fine-scale statistics for the multidimensional Farey sequence -- S. G. Bobkov, M. M. Madiman: On the problem of reversibility of the entropy power inequality -- G. P. Chistyakov: On probability measures with unbounded angular ratio -- M. Gordin: CLT for stationary normal Markov chains via generalized coboundaries -- T. Mai, R. Speicher: Operator-valued and multivariate free Berry-Esseen theorems -- T. Mai, R. Speicher: Operator-valued and multivariate free Berry-Esseen theorems -- R. Bhattacharya: A nonparametric theory of statistics on manifolds -- J. Lember, H. Matzinger, F. Torres: Proportion of gaps and uctuations of the optimal score in random sequence comparison -- Y. V. Prokhorov, V. V. Ulyanov: Some approximation problems in statistics and probability -- H. Döring, P. Eichelsbacher: Moderate deviations for the determinant of Wigner matrices -- O. Friesen, M. Löwe: The semicircle law for matrices with dependent entries -- A. Tikhomirov: Limit theorems for random matrices.
Content:
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.
Note:
Includes bibliographical references
,
Preface; Contents; A Conversation with Friedrich Götze; 1 Early Days: A Talented Tinkerer; 2 A Wander-Student; 3 To the USA and Back; 4 Bielefeld; 5 Oberwolfach; 6 Relations with Eastern Europe; 7 German Reunification; 8 Visiting Committees; 9 Scientific Interests; Part I Number Theory; Distribution of Algebraic Numbers and Metric Theory of Diophantine Approximation; 1 Introduction; 2 Distribution of Discriminants of Integral Polynomials; 2.1 Sketch of the Proof of Theorem 5; 2.2 Sketch of the Proof of Theorem 6; 3 Divisibility of Discriminants by Prime Powers
,
4 Close Conjugate Algebraic Numbers5 On the Distribution of Resultants; References; Fine-Scale Statistics for the Multidimensional Farey Sequence; References; Part II Probability Theory; On the Problem of Reversibility of the Entropy Power Inequality; 1 The Reversibility Problem for the Entropy Power Inequality; 2 A ``Difference Measure'' Inequality for Convex Measures; 3 Proof of Theorem 1.3; 4 Remarks; References; On Probability Measures with Unbounded Angular Ratio; 1 Introduction; 2 Results; 3 Proof of Theorem 2.1; 4 Discussion of Theorem 2.1; 5 Proof of Theorems 2.15 and 2.16; References
,
CLT for Stationary Normal Markov Chains via Generalized Coboundaries1 Introduction; 2 Contractions, Transition Operators and Markov Chains; 2.1 Some Notation; 2.2 Normal Contractions; 2.3 Unitary Part of a Transition Operator and Its Deterministic σ-Field; 2.4 Defect Operators and Defect Spaces of a Contraction; 3 Quasi-functions; 3.1 Quasi-functions: m-Functions and t-Functions; 3.2 Functions and m-Functions; 3.3 Functions and t-Functions; 4 The CLT; References; Operator-Valued and Multivariate Free Berry-Esseen Theorems; 1 Introduction; 2 Holomorphic Functions on Domains in Banach Spaces
,
3 Matrix-Valued Spectra and Cauchy Transforms4 Multivariate Free Central Limit Theorem; 4.1 Setting and First Observations; 4.2 Proof of the Main Theorem; 4.3 Application to Multivariate Situation; 4.3.1 Multivariate Free Central Limit Theorem; 4.3.2 Estimates in Terms of the Kolmogorov Distance; References; A Characterization of Small and Large Time Limit Laws for Self-normalized Lévy Processes; 1 Introduction and Statements of Main Results; 1.1 Some Needed Technical Results; 2 Proofs of Theorems; 2.1 Proof of Theorem 1.2; 2.2 Proof of Theorem 1.1; 3 Proofs of Propositions 1.1 and 1.2
,
3.1 Proof of Proposition 1.13.2 Proof of Proposition 1.2; 3.2.1 Comments on Proofs of Propositions 3.1 and 3.2; 4 Appendix: Strictly Stable Bivariate Laws; References; Part III Statistics and Combinatorics; A Nonparametric Theory of Statistics on Manifolds; 1 Introduction; 2 Asymptotic Distribution Theory for Fréchet Means; 3 Asymptotic Distribution of the Extrinsic Sample Mean on a Manifold; 4 Asymptotic Distribution of the Intrinsic Sample Mean and the Role of Curvature; 5 Nonparametric Inference on General Manifolds; 6 Geometry of Shape Spaces and Equivariant Embeddings
,
6.1 Kendall's Similarity Shape Space Σmk
,
W. van Zwet: A conversation with Friedrich Götze -- V. Bernik, V. Beresnevich, F. Götze, O. Kukso: Distribution of algebraic numbers and metric theory of Diophantine approximation -- J. Marklof: Fine-scale statistics for the multidimensional Farey sequence -- S. G. Bobkov, M. M. Madiman: On the problem of reversibility of the entropy power inequality -- G. P. Chistyakov: On probability measures with unbounded angular ratio -- M. Gordin: CLT for stationary normal Markov chains via generalized coboundaries -- T. Mai, R. Speicher: Operator-valued and multivariate free Berry-Esseen theorems -- T. Mai, R. Speicher: Operator-valued and multivariate free Berry-Esseen theorems -- R. Bhattacharya: A nonparametric theory of statistics on manifolds -- J. Lember, H. Matzinger, F. Torres: Proportion of gaps and uctuations of the optimal score in random sequence comparison -- Y. V. Prokhorov, V. V. Ulyanov: Some approximation problems in statistics and probability -- H. Döring, P. Eichelsbacher: Moderate deviations for the determinant of Wigner matrices -- O. Friesen, M. Löwe: The semicircle law for matrices with dependent entries -- A. Tikhomirov: Limit theorems for random matrices.
Additional Edition:
ISBN 9783642360671
Additional Edition:
Druckausg. Limit theorems in probability, statistics and number theory Berlin : Springer, 2013 ISBN 364236067X
Additional Edition:
ISBN 9783642360671
Language:
English
Subjects:
Economics
,
Mathematics
Keywords:
Grenzwertsatz
;
Asymptotische Entwicklung
;
Grenzwertsatz
;
Wahrscheinlichkeitstheorie
;
Zahlentheorie
;
Konferenzschrift
DOI:
10.1007/978-3-642-36068-8
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
