Random evolution denotes a class of stochastic processes which evolve according to a rule which varies in time according to jumps. This is in contrast to diffusion processes, which assume that the rule changes continuously with time. Random evolutions provide a very flexible language, having the advantage that they permit direct numerical simulation-which is not possible for a diffusion process. Furthermore, they allow connections with hyperbolic partial differential equations and the kinetic theory of gases, which is impossible within the domain of diffusion proceses. They also posses great geometric invariance, allowing formulation on an arbitrary Riemannian manifold. In the field of stochastic stability, random evolutions furnish some easily computable models in which to study the Lyapunov exponent and rotation numbers of oscillators under the influence of noise. This monograph presents the various aspects of random evolution in an accessible and interesting format which will appeal to a large scientific audience.

This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach.

New York Times bestseller • Winner of the Los Angeles Times Book Prize • One of the Washington Post's 10 Best Books of the Year “It’s no exaggeration to say that Behave is one of the best nonfiction books I’ve ever read.” —David P. Barash, The Wall Street Journal "It has my vote for science book of the year.” —Parul Sehgal, The New York Times "Immensely readable, often hilarious...Hands-down one of the best books I’ve read in years. I loved it." —Dina Temple-Raston, The Washington Post From the bestselling author of A Primate's Memoir and the forthcoming Determined: A Science of Life Without Free Will comes a landmark, genre-defining examination of human behavior and an answer to the question: Why do we do the things we do? Behave is one of the most dazzling tours d’horizon of the science of human behavior ever attempted. Moving across a range of disciplines, Sapolsky—a neuroscientist and primatologist—uncovers the hidden story of our actions. Undertaking some of our thorniest questions relating to tribalism and xenophobia, hierarchy and competition, and war and peace, Behave is a towering achievement—a majestic synthesis of cutting-edge research and a heroic exploration of why we ultimately do the things we do . . . for good and for ill.

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.

First comprehensive, beginning graduate level book on the emergent science of astrobiology.