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Random Signals

Random Signals

K. Sam Shanmugan; Arthur M. Breipohl

John Wiley Sons Inc
1988
nidottu
Random Signals, Noise and Filtering develops the theory of random processes and its application to the study of systems and analysis of random data. The text covers three important areas: (1) fundamentals and examples of random process models, (2) applications of probabilistic models: signal detection, and filtering, and (3) statistical estimation--measurement and analysis of random data to determine the structure and parameter values of probabilistic models. This volume by Breipohl and Shanmugan offers the only one-volume treatment of the fundamentals of random process models, their applications, and data analysis.
Random Violence

Random Violence

Joel Best

University of California Press
1999
pokkari
"Random Violence" is a deft and thought-provoking exploration of the ways we talk about - and why we worry about - new crimes and new forms of victimization. Focusing on so-called random crimes such as freeway shootings, gang violence, hate crimes, stalking, and wilding, Joel Best shows how new crime problems emerge and how some quickly fade from public attention while others spread and become enduring subjects of concern. Best's original and incisive argument illuminates the fact that while these crimes are in actuality neither new, nor epidemic, nor random, the language used to describe them nonetheless shapes both private fears and public policies. Best scrutinizes the melodramatic quality of the American public's attitudes toward crime, exposing the cultural context for the popularity of 'random violence' as a catch-all phrase to describe contemporary crime, and the fallacious belief that violence is steadily rising. He points out that the age, race, and sex of homicide victims reveal that violence is highly patterned. Best also details the contemporary ideology of victimization, as well as the social arrangements that create and support a victim industry that can label large numbers of victims. He demonstrates why it has become commonplace to 'declare war' on social problems, including drugs, crime, poverty, and cancer, and outlines the complementary influence of media, activists, officials, and experts in institutionalizing crime problems. Intrinsic to all these concerns is the way in which policy choices and outcomes are affected by the language used to describe social problems.
Random Walks on Infinite Graphs and Groups

Random Walks on Infinite Graphs and Groups

Woess Wolfgang

Cambridge University Press
2008
pokkari
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Random Graphs

Random Graphs

V. F. Kolchin

Cambridge University Press
2009
pokkari
This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the study of random graphs and permutations reduces the combinatorial problems to classical problems of probability theory on the summation of independent random variables. He concentrates on research by Russian mathematicians, including a discussion of equations containing an unknown permutation and a presentation of techniques for solving systems of random linear equations in finite fields. These results will interest specialists in combinatorics and probability theory and will also be useful in applied areas of probabilistic combinatorics such as communication theory, cryptology, and mathematical genetics.
Random Matrices: High Dimensional Phenomena

Random Matrices: High Dimensional Phenomena

Gordon Blower

Cambridge University Press
2009
pokkari
This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
Random Fields and Spin Glasses

Random Fields and Spin Glasses

Cirano De Dominicis; Irene Giardina

Cambridge University Press
2010
pokkari
Disordered magnetic systems enjoy non-trivial properties which are different and richer than those observed in their pure, non-disordered counterparts. These properties dramatically affect the thermodynamic behaviour and require specific theoretical treatment. This book deals with the theory of magnetic systems in the presence of frozen disorder, in particular paradigmatic and well-known spin models such as the Random Field Ising Model and the Ising Spin Glass. This is a unified presentation using a field theory language which covers mean field theory, dynamics and perturbation expansion within the same theoretical framework. Particular emphasis is given to the connections between different approaches such as statics vs. dynamics, microscopic vs. phenomenological models. The book introduces some useful and little-known techniques in statistical mechanics and field theory. This book will be of great interest to graduate students and researchers in statistical physics and basic field theory.
Random Graph Dynamics

Random Graph Dynamics

Rick Durrett

Cambridge University Press
2010
pokkari
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Random Matrix Models and their Applications
Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This 2001 volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its stress on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis.
Random Fields on the Sphere

Random Fields on the Sphere

Domenico Marinucci; Giovanni Peccati

Cambridge University Press
2011
pokkari
Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3). Many recent developments on the method of moments and cumulants for the analysis of Gaussian subordinated fields are reviewed. This background material is used to analyse spectral representations of isotropic spherical random fields and then to investigate in depth the properties of associated harmonic coefficients. Properties and statistical estimation of angular power spectra and polyspectra are addressed in full. The authors are strongly motivated by cosmological applications, especially the analysis of cosmic microwave background (CMB) radiation data, which has initiated a challenging new field of mathematical and statistical research. Ideal for mathematicians and statisticians interested in applications to cosmology, it will also interest cosmologists and mathematicians working in group representations, stochastic calculus and spherical wavelets.
Random Graphs

Random Graphs

V. F. Kolchin

Cambridge University Press
1998
sidottu
This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the study of random graphs and permutations reduces the combinatorial problems to classical problems of probability theory on the summation of independent random variables. He concentrates on recent research by Russian mathematicians, including a discussion of equations containing an unknown permutation and the first English-language presentation of techniques for solving systems of random linear equations in finite fields. These new results will interest specialists in combinatorics and probability theory and will also be useful in applied areas of probabilistic combinatorics such as communication theory, cryptology, and mathematical genetics.
Random Walk: A Modern Introduction

Random Walk: A Modern Introduction

Gregory F. Lawler; Vlada Limic

Cambridge University Press
2010
sidottu
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Random Dynamical Systems

Random Dynamical Systems

Rabi Bhattacharya; Mukul Majumdar

Cambridge University Press
2007
pokkari
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.
Random Walks on Infinite Graphs and Groups

Random Walks on Infinite Graphs and Groups

Woess Wolfgang

Cambridge University Press
2000
sidottu
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally-finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Random Variables and Probability Distributions

Random Variables and Probability Distributions

H. Cramer

Cambridge University Press
2004
pokkari
This tract develops the purely mathematical side of the theory of probability, without reference to any applications. When originally published, it was one of the earliest works in the field built on the axiomatic foundations introduced by A. Kolmogoroff in his book Grundbegriffe der Wahrscheinlichkeitsrechnung, thus treating the subject as a branch of the theory of completely additive set functions. The author restricts himself to a consideration of probability distributions in spaces of a finite number of dimensions, and to problems connected with the Central Limit Theorem and some of its generalizations and modifications. In this edition the chapter on Liapounoff’s theorem has been partly rewritten, and now includes a proof of the important inequality due to Berry and Esseen. The terminology has been modernized, and several minor changes have been made.
Random Matrix Models and their Applications
Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This 2001 volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its stress on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis.
Random Graphs

Random Graphs

Béla Bollobás

Cambridge University Press
2001
sidottu
In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.