An Unbounded Experience in Random Walks with Applications (Hardcover)

An Unbounded Experience in Random Walks with Applications By Michael F. Shlesinger Cover Image

An Unbounded Experience in Random Walks with Applications (Hardcover)

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This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul L vy's work via Mandelbrot's L vy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.
Product Details ISBN: 9789811232800
ISBN-10: 9811232806
Publisher: World Scientific Publishing Company
Publication Date: July 14th, 2021
Pages: 216
Language: English