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Unbounded Experience In Random Walks With Applications, An (Hardcover)
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Unbounded Experience In Random Walks With Applications, An (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 Levy's work
via Mandelbrot's Levy 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.
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