Random Summation

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.

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 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.

This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of i

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory.

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory.

A visual celebration of Italian luxury and the essence of design sensibility. The Altagamma Foundation was created in 1992 to gather under one umbrella Italian companies whose brands are known internationally for excellence. Altagamma promotes Italian industry and the traditional culture that sustains it. The companies included are all prized for innovation, quality, service, design, and prestige, and include Bulgari, Driade, Ermenegildo Zegna, Gucci, Illy, Tod's, and Persol—just to name a few. To mark the twentieth anniversary of the Altagamma Foundation, this lavishly illustrated volume celebrates Italy's most significant brands through the work of Magnum Photo and Contrasto Agency's most important photographers, including Paolo Pellegrin, Alex Majoli, Massimo Siragusa, Lorenzo Cicconi Massi, Daniele Dainelli, and Marta Sarlo, among others. In these images, each brand is no longer just an icon of luxury, but becomes a summation of something uniquely Italian: a synthesis of culture,