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Author:   Ariel Amir (Harvard University, Massachusetts)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Dimensions:   Width: 17.00cm , Height: 1.50cm , Length: 24.30cm
Weight:   0.440kg
ISBN:  

9781108789981

ISBN 10:   1108789986
Pages:   242
Publication Date:   17 December 2020
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

1. Introduction; 2. Random walks; 3. Langevin and Focker–Planck equations and their applications; 4. Escape over a barrier; 5. Noise; 6. Generalized central limit theorem and extreme value statistics; 7. Anomalous diff usion; 8. Random matrix theory; 9. Percolation theory; Appendix A. Review of basic probability concepts and common distributions; Appendix B. A brief linear algebra reminder, and some Gaussian integrals; Appendix C. Contour integration and Fourier transform refresher; Appendix D. Review of Newtonian mechanics, basic statistical mechanics and Hessians; Appendix E. Minimizing functionals, the divergence theorem and saddle point approximations; Appendix F. Notation, notation...; References; Index.

Reviews

'A remarkable demonstration that advanced topics need not be esoteric. Amir takes us through random walks on networks, extreme value statistics, Kramers theory, anomalous diffusion and other topics generally omitted from introductory texts, always rooting every discussion in applications of terrific current interest. I found the discussion of Levy-stable distributions especially insightful as a principled approach to the nonstandard walks that abound in contexts from biophysics to finance.' Philip C. Nelson, University of Pennsylvania

'A remarkable demonstration that advanced topics need not be esoteric. Amir takes us through random walks on networks, extreme value statistics, Kramers theory, anomalous diffusion and other topics generally omitted from introductory texts, always rooting every discussion in applications of terrific current interest. I found the discussion of Levy-stable distributions especially insightful as a principled approach to the nonstandard walks that abound in contexts from biophysics to finance.' Philip C. Nelson, University of Pennsylvania 'A remarkable demonstration that advanced topics need not be esoteric. Amir takes us through random walks on networks, extreme value statistics, Kramers theory, anomalous diffusion and other topics generally omitted from introductory texts, always rooting every discussion in applications of terrific current interest. I found the discussion of Levy-stable distributions especially insightful as a principled approach to the nonstandard walks that abound in contexts from biophysics to finance.' Philip C. Nelson, University of Pennsylvania

Author Information

Ariel Amir is a Professor at Harvard University, Massachusetts. His research centers on the theory of complex systems.

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