Brownian Agents and Active Particles

From the reviews:

"Schweitzer's approach is gradual. The first four chapters are devoted to introducing more and more complexities and subtleties in the Brownian agent models, and the focus is on the models themselves rather than on the systems... Reading and understanding these chapters may be a difficult time-consuming task, but the reward is high. Starting from chapter five (on tracks and trail formation in biological systems) and ending with chapter ten (on opinion formation), the reader can amuse him/herself in dealing with models of real systems and devote his/her attention to the more relevant issues for his/her research.

"This book contains some gems. My favorite one is in chapter nine: the discussion of a spatial dynamic model for the labor market introduced by the well-known US economist Paul Krugman where "workers are assumed to move toward locations that offer them higher real wages". Schweitzer shows not only that Krugman's model is nothing else that an instance of a selection equation of the Fisher-Eigen type, but also, using the formalism developed previously, he can easily generalize it and question the economic meaning of the assumptions leading to Krugman's equations.

"I can recommend this book to all those working in the field of complex systems. They will find a detailed survey of the Brownian agent method and they might get good hints for further research in some of the fascinating fields herein discussed."

- Enrico Scalas (econophysics.org)

"[...] the author explores such diverse topics as pattern formation in reaction diffusion systems, self organisations of networks, tracks and trail formations in biological systems, movement and trail formation by pedestrians, urban aggregation, economic aggregations and spatial opinion structures in social systems. The topics are selected thoughtfully and the presentation is lucid. It is an extremely useful text for graduate students who arethinking of working on some problem in non equilibrium statistical physics." (Jayanta K. Bhattacharjee, Indian Journal of Physics 2004, vol. 78, page 1011)

"This book is organized around two ideas. First, the link between the micro- and the macro-behaviour of systems and secondly, the idea of a Brownian agent. ... Many of these models and ideas have been circulating for some time and will be found in specialist publications. It is helpful to have them brought together and systematically expounded in this book which both unifies what exists and paves the way for new developments." (Professor D. J. Bartholomew, Contemporary Physics, Vol. 45 (4), 2004)

"The aim of the book is to show that a large set of phenomena in natural and social sciences can be studied by writing down equations of motion for the pertinent Brownian agents. ... The topics are selected thoughtfully and the presentation is lucid. It is an extremely useful text for graduate students who are thinking of working on some problem in non equilibrium statistical physics." (Jayanta K Bhattacharjee, Indian Journal of Physics, Vol. 78 (9), 2004)