# random matrices and random partitions normal convergence world scientific series on probability theory and its applications

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## Random Matrices And Random Partitions

**Author :**Zhonggen Su

**ISBN :**9789814612241

**Genre :**Mathematics

**File Size :**24. 14 MB

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This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of various eigenvalue statistics. This is attributed to the nice algebraic structures of models. This part also studies the Circular β Ensembles and Hermitian β Ensembles. Part III is devoted to the study of random uniform and Plancherel partitions. There is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models. A remarkable point is the conditioning argument in each model. Through enlarging the probability space, we run into independent geometric random variables as well as determinantal point processes with discrete Bessel kernels. This book treats only second-order normal fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes. Contents:Normal ConvergenceCircular Unitary EnsembleGaussian Unitary EnsembleRandom Uniform PartitionsRandom Plancherel Partitions Readership: Graduates and researchers majoring in probability theory and mathematical statistics, especially for those working on Probability Limit Theory. Key Features:The book treats only two special models of random matrices, that is, Circular and Gaussian Unitary Ensembles, and the focus is on second-order fluctuations of primary eigenvalue statistics. So all theorems and propositions can be stated and proved in a clear and concise languageIn a companion part, the book also treats two special models of random integerpartitions, namely, random uniform and Plancherel partitions. It exhibits a surprising similarity between random matrices and random partitions from the viewpoint of asymptotic distribution theory, though there is no direct link between finite modelsThe limit distributions of most statistics of interest are obtained by reducing to classical central limit theorems for sums of independent random variables, martingale sequences and Markov chains. So the book is easily accessible to readers that are familiar with a standard probability theory textbookKeywords:Central Limit Theorems;Random Matrices;Random Partitions

## An Introduction To The Theory Of Probability

**Author :**Parimal Mukhopadhyay

**ISBN :**9789814313421

**Genre :**Mathematics

**File Size :**88. 18 MB

**Format :**PDF, ePub

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The Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution and convergence of random variables. Difficult ideas have been explained lucidly and have been augmented with explanatory notes, examples and exercises. The basic requirement for reading this book is simply a knowledge of mathematics at graduate level. This book tries to explain the difficult ideas in the axiomatic approach to the theory of probability in a clear and comprehensible manner. It includes several unusual distributions including the power series distribution that have been covered in great detail. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging. The author is a former Professor of the Indian Statistical Institute, India.

## Statistical Experiments And Decisions

**Author :**A N Shiryaev

**ISBN :**9789814494151

**Genre :**Mathematics

**File Size :**67. 15 MB

**Format :**PDF

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This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”. Contents:Statistical Experiments and Their ComparisonConvergence of Statistical Experiments(γ,Γ)-Models. Convergence to (γ,Γ)-ModelsLocal Convergence of Statistical Experiments and Global EstimationStatistical Inference for Autoregressive Models of the First Order Readership: Researchers in probability and statistics. Keywords:Comparison of Statistical Experiments;Mixed Local Asymptotic Normality;Convergence of Experiments;Likelihood Ratio Processes;Contiguity;Autoregressive Models;Minimax Bound;Local Asymptotic NormalityReviews: “It is an interesting, welcome addition to the literature, and it contains many new insights. I congratulate the authors for writing this comprehensive monograph on a difficult subject.” Mathematical Reviews “The book is a highlight in modern mathematical statistics which offers a lot of new concepts. It recalls the brilliant methodology of Le Cam's Theory and the first chapters may be used as introduction into this field.” Mathematics Abstracts

## A First Course In Probability And Statistics

**Author :**B. L. S. Prakasa Rao

**ISBN :**9789812836533

**Genre :**Mathematics

**File Size :**30. 46 MB

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This book provides a clear exposition of the theory of probability along with applications in statistics.

## The Stress Strength Model And Its Generalizations

**Author :**Samuel Kotz

**ISBN :**9812564519

**Genre :**Mathematics

**File Size :**34. 66 MB

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This important book presents developments in a remarkable field ofinquiry in statistical/probability theory the stressOCostrengthmodel.Many papers in the field include the enigmatic words"P"("X"Y") or something similar in thetitle."

## Probability Finance And Insurance

**Author :**T. L. Lai

**ISBN :**9789812388537

**Genre :**Mathematics

**File Size :**87. 1 MB

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This workshop was the first of its kind in bringing together researchers in probability theory, stochastic processes, insurance and finance from mainland China, Taiwan, Hong Kong, Singapore, Australia and the United States. In particular, as China has joined the WTO, there is a growing demand for expertise in actuarial sciences and quantitative finance. The strong probability research and graduate education programs in many of China's universities can be enriched by their outreach in fields that are of growing importance to the country's expanding economy, and the workshop and its proceedings can be regarded as the first step in this direction.This book presents the most recent developments in probability, finance and actuarial sciences, especially in Chinese probability research. It focuses on the integration of probability theory with applications in finance and insurance. It also brings together academic researchers and those in industry and government. With contributions by leading authorities on probability theory ? particularly limit theory and large derivations, valuation of credit derivatives, portfolio selection, dynamic protection and ruin theory ? it is an essential source of ideas and information for graduate students and researchers in probability theory, mathematical finance and actuarial sciences, and thus every university should acquire a copy.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? Index to Social Sciences & Humanities Proceedings? (ISSHP? / ISI Proceedings)? Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

## Probability Theory

**Author :**Nikolai Dokuchaev

**ISBN :**9789814678056

**Genre :**Business & Economics

**File Size :**21. 31 MB

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This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

## Mathematical Methods In Sample Surveys

**Author :**Howard G Tucker

**ISBN :**9789814499170

**Genre :**Mathematics

**File Size :**82. 12 MB

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This book is about both the mathematics of sample surveys and about sample surveys. The mathematics is both elementary and rigorous. It is suitable for a one year junior-senior level course for mathematics and statistics majors as well as for students in the social sciences who are not handicapped by a fear of proofs in mathematics. It requires no previous knowledge of statistics, and it could actually serve as an introduction to statistics. A sizeable part of the book covers the discrete probability needed for the sampling methods covered. Topics then covered are: simple random sampling, sampling with unequal probabilities, linear relationships, stratified sampling, cluster sampling and two-stage sampling. Contents:Events and ProbabilityRandom VariablesExpectationConditional ExpectationLimit TheoremsSimple Random SamplingUnequal Probability SamplingLinear RelationshipsStratified SamplingCluster SamplingTwo-Stage Sampling Readership: Mathematical statisticians. keywords:Discrete Probability;Simple Random Sampling;Unequal Probability Sampling;Stratified Sampling;Cluster Sampling;Two-Stage Sampling;Ratio Estimation “The book is well written and could serve as a very good supplement to more traditional courses in mathematical statistics. It could also be recommended to interested students as a supplementary reading.” Mathematical Reviews

## Random Sequential Packing Of Cubes

**Author :**

**ISBN :**9789814464789

**Genre :**

**File Size :**39. 17 MB

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## Elements Of Stochastic Modelling

**Author :**Konstantin Borovkov

**ISBN :**9789814571180

**Genre :**Mathematics

**File Size :**67. 45 MB

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This is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material. Request Inspection Copy