Central Limit Theorem, Random Walk, Brownian Motion

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EinsteinCLT andRandomWalkJeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotionEinstein explained these ideas(1905)Showed that “according to thelaws of molecular-kinetic theoryof heat, bodies of amicroscopically visible sizesuspended in a liquid must as aresult of thermal molecularmotions, perform motion visibleunder a microscope”
Einstein’s ExplanationCLT andRandomWalkJeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotionResulting theory allowed Einstein to calculuateAvogadro’s number from the observed diffusion ofgrains.Experimentally verified by Jean PerrinEinstein assumed that:the particles of pollen were hit many times bymuch smaller particleEach collision produces a small change indirection and speedEach collision is essentially randomDifferent collisions are independentTHIS IS A RANDOM WALK! (in three dimensions)
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Gambler’s RuinCLT andRandomWalkJe
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Central Limit Theorem, Random Walk, Brownian Motion

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