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Random Graph Dynamics

2010-05-31 Mathematics
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Release : 2010-05-31
Genre : Mathematics
Kind : eBook
Book Rating : 889/5 ( reviews)

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Book Synopsis Random Graph Dynamics by : Rick Durrett

Download or read book Random Graph Dynamics written by Rick Durrett. This book was released on 2010-05-31. Available in PDF, EPUB and Kindle. Book excerpt: 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 Dynamical Systems

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 780/5 ( reviews)

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Book Synopsis Random Dynamical Systems by : Ludwig Arnold

Download or read book Random Dynamical Systems written by Ludwig Arnold. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Dynamics and Randomness

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 459/5 ( reviews)

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Book Synopsis Dynamics and Randomness by : Alejandro Maass

Download or read book Dynamics and Randomness written by Alejandro Maass. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book.

Dynamics of Gambling: Origins of Randomness in Mechanical Systems

2010-01-14 Science
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Release : 2010-01-14
Genre : Science
Kind : eBook
Book Rating : 60X/5 ( reviews)

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Book Synopsis Dynamics of Gambling: Origins of Randomness in Mechanical Systems by : Jaroslaw Strzalko

Download or read book Dynamics of Gambling: Origins of Randomness in Mechanical Systems written by Jaroslaw Strzalko. This book was released on 2010-01-14. Available in PDF, EPUB and Kindle. Book excerpt: Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.

P-adic Deterministic and Random Dynamics

2013-03-14 Science
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Release : 2013-03-14
Genre : Science
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis P-adic Deterministic and Random Dynamics by : Andrei Y. Khrennikov

Download or read book P-adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

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