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Level: BSc, MSci
Title: Spitzer's identity
Supervisor:

Dr Rosemary Harris
Research Area: Dynamical Systems and Statistical Physics
Description:

Spitzer's identity is a classical result which connects the probability distribution of the maxima of a random walk with the probability distribution of the walk itself. The project is to understand the result and present one or more proofs of it (at least for the case of right-continuous walks as treated, for example, in Grimmett and Stirzaker [1]). The student could also give an exposition of some generalizations/consequences of Spitzer's identity and/or test it numerically.

  1. G. Grimmett, D. Stirzaker, Probability and Random Processes. Oxford Univ. Press, 2001.
Further Reading:
  • F. Spitzer, A combinatorial lemma and its application to probability theory, Trans. Amer. Math. Soc. 82 (1956) 323–339.
Key Modules:

MTH6141 Random Processes

MTH6934/MTH734U/MTHM012/MTH712P Topics in Probability and Stochastic Processes
Other Information:
Current Availability: Yes