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RESEARCH PRODUCT

Random Walk and Diffusion

Walter Schirmacher

subject

symbols.namesakePartial differential equationHeterogeneous random walk in one dimensionDiffusion equationFourier transformLaplace transformDifferential equationMathematical analysissymbolsEinsteinRandom walkMathematics

description

The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.

yearjournalcountryeditionlanguage
2014-05-19
https://doi.org/10.1007/978-3-319-06950-0_4