The Central Limit Theorem

  • George D.J. Phillies
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


If one observes—via a high-power microscope—an equilibrium suspension or solution of nanometer-to-micron scale particles, one finds that the particles do not remain stationary. Instead, the particles perform an irregular jittering motion. Over long periods of time, this motion allows the particles to translate through large distances. The irregular jittering is named Brownian motion in honor of Robert Brown, an English clergyman who in the nineteenth century was the first to report [1] this motion and describe its properties.


Brownian Motion Characteristic Function Central Limit Theorem Langevin Equation Brownian Particle 
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  1. [1]
    Whether one can see Brown’s effects with Brown’s instrument has recently become a topic of controversy, with multiple reports in Nature.Google Scholar
  2. [2]
    “Consider this small dust, here in the glass by atoms moved”, The Hour Glass by Ben Jonson (1573-1637), as quoted by K. S. Schmitz, An Introduction to Dynamic Light Scattering by Macromolecules, Academic Press, San Diego, (1990).Google Scholar
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    J. G. Kirkwood and J. Riseman, J. Chem. Phys. 16, 565 (1948). See also A. Altenberger andJ. M. Deutch, J. Chem. Phys. 59, 894 (1973).ADSCrossRefGoogle Scholar
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    J. C. Crocker, J. Chem. Phys. 106, 2837 (1997); J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352 (1994); J. C. Crocker and D. G. Grier, J. Colloid Interf. Sci. 179, 298 (1996).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • George D.J. Phillies
    • 1
  1. 1.Department of Physics and Associated Biochemistry FacultyWorcester Polytechnic InstituteWorcesterUSA

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