1999
DOI: 10.1590/s0103-97331999000300014
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Brownian motion limit of random walks in symmetric non-homogeneous media

Abstract: The phenomenon of macroscopic homogenization is illustrated with a simple example of di usion. We examine the conditions under which a d dimensional simple random walk in a symmetric random media converges to a Brownian motion. For d = 1, both the macroscopic homogeneity condition and the di usion coe cient can be read from an explicit expression for the Green's function. Except for this case, the two a vailable formulas for the e ective di usion matrix do not explicit show h o w macroscopic homogenization tak… Show more

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Cited by 3 publications
(3 citation statements)
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“…It is well known that the limit as n → ∞ of the random walk is the Wiener process in D dimensions [3]. We exploit this property to establish the characterisation of the constrained Wiener process in continuous time.…”
Section: Characterisation Of Extremamentioning
confidence: 99%
“…It is well known that the limit as n → ∞ of the random walk is the Wiener process in D dimensions [3]. We exploit this property to establish the characterisation of the constrained Wiener process in continuous time.…”
Section: Characterisation Of Extremamentioning
confidence: 99%
“…Examples can be found as disordered linear chains generated by arbitrary mass and spring-constants [1], random walks in random environments and diffusion (see for example Refs. [2][3][4]), charge trapping phenomena (electron transport) in semiconductor devices (see for example Refs. [5][6][7][8][9][10][11]), and transport of molecules (chromatography) in chemistry [12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…A large number of stochastic phenomena in literature are related to the passage of particles through random media generated, for example, by imperfections of the environment. Examples can be found as disordered linear chains generated by arbitrary mass and springconstants 1 , random walks in random environments and diffusion (see for example [2][3][4] , charge trapping phenomena (electron transport) in semiconductor devices (see for example [6][7][8][9][10][11] ), and transport of molecules (chromatography) in Chemistry ( [12][13][14] ).…”
mentioning
confidence: 99%