Complexity Explorer

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About the Tutorial:

This tutorial introduces Random Walks.  Note that Complexity Explorer tutorials are meant to introduce students to various important techniques and to provide illustrations of their application in complex systems.  A given tutorial is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.   

This tutorial is designed for more advanced math students.  Math prerequisites for this course are an understanding of calculus, basic probability, and Fourier transforms.


About the Instructor(s):

Sid Redner is a Resident Faculty Member at the Santa Fe Institute. 

Sid Redner received an A.B. in physics from the University of California, Berkeley in 1972 and a Ph.D. in Physics from MIT in 1977.  After a postdoctoral year at the University of Toronto, Sid joined the physics faculty at Boston University in 1978.  During his 36 years at BU, he served as Acting Chair during two separate terms and also served as Departmental Chair.  Sid has been a Visiting Scientist at Schlumberger-Doll Research in the mid 80's, the Ulam Scholar at LANL in 2004, and a sabbatical visitor at Université Paul Sabatier in Toulouse France and at Université Pierre-et-Marie-Curie in Paris.

Sid has published more than 250 articles in major peer-reviewed journals, as well as two books: the monograph A Guide to First-Passage Processes (Cambridge Univ. Press, 2001) and the graduate text, jointly with P. L. Krapivsky and E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge Univ. Press, 2010).  He also a member of the Editorial Board for the Journal of Informetrics, an Associate Editor for the Journal of Statistical Physics, and a Divisional Associate Editor for Physical Review Letters.   For more on Sid, visit his website.  Read a Q&A with Sid on his Random Walks tutorial here

How to use Complexity Explorer
Enrolled students:



Calculus; Basic Probability; Fourier Transforms

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5 Student


  1. Introduction
  2. Root Mean Square Displacement
  3. Role of the Spatial Dimension
  4. Probability Distribution and Diffusion Equation
  5. Central Limit Theorem
  6. First Passage Phenomena
  7. Elementary Applications of First Passage Phenomena
  8. Final Remarks
  9. Homework