Random Numbers and Monte Carlo Methods

  • Philipp O. J. Scherer
Part of the Graduate Texts in Physics book series (GTP)


Many-body problems often involve the calculation of integrals of very high dimension which cannot be treated by standard methods. For the calculation of thermodynamic averages Monte Carlo methods are very useful which sample the integration volume at randomly chosen points. After summarizing some basic statistics, we discuss algorithms for the generation of pseudo-random numbers with given probability distribution which are essential for all Monte Carlo methods. We show how the efficiency of Monte Carlo integration can be improved by sampling preferentially the important configurations. Finally the famous Metropolis algorithm is applied to classical many-particle systems. Computer experiments visualize the central limit theorem and apply the Metropolis method to the traveling salesman problem.


Partition Function Cumulative Distribution Function Travel Salesman Problem Pseudo Random Number Monte Carlo Integration 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Philipp O. J. Scherer
    • 1
  1. 1.Physikdepartment T38Technische Universität MünchenGarchingGermany

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