Difference between revisions of "Random Walks"

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(Created page with '===Short Topical Videos=== * [http://youtu.be/-BuiT39WUHY The Radiative Scattering of Light: the Basics (by Aaron Parsons)] ===Reference Material=== * [https://en.wikipedia.org…')
 
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===Short Topical Videos===
 
===Short Topical Videos===
* [http://youtu.be/-BuiT39WUHY The Radiative Scattering of Light: the Basics (by Aaron Parsons)]
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* [http://youtu.be/-BuiT39WUHY The Random Walk (by Aaron Parsons)]
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* [https://www.youtube.com/watch?v=nWPwKA_1ANk Physics Demonstrations by Sprott, Chapter 1, Motion, Demo 1.21 Random Walk (Sprott, U. Wisconsin)]
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* [https://www.youtube.com/watch?v=pdz7wFHSLD0 Brownian Motion (mathslug, YouTube)]
  
 
===Reference Material===
 
===Reference Material===
 
* [https://en.wikipedia.org/wiki/Random_walk Random Walk (Wikipedia)]
 
* [https://en.wikipedia.org/wiki/Random_walk Random Walk (Wikipedia)]
 
* [http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/random.htm Random Walks: the Mathematics in One Dimension (Kardar, MIT)]
 
* [http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/random.htm Random Walks: the Mathematics in One Dimension (Kardar, MIT)]
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* [http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/RandomWalk.pdf The One-Dimensional Random Walk (Fowler, UVa)]
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* [http://www.feynmanlectures.caltech.edu/I_06.html The Feynman Lectures, CH 6-3 (Feynman, Caltech)]
  
 
<latex>
 
<latex>

Revision as of 14:46, 31 August 2016

Short Topical Videos

Reference Material

<latex> \documentclass[11pt]{article} \def\inv#1Template:1 \over \def\ddtTemplate:D \over dt \def\mean#1{\left\langle #1\right\rangle} \def\sigot{\sigma_{12}} \def\sigto{\sigma_{21}} \def\eval#1{\big|_{#1}} \def\tr{\nabla} \def\dce{\vec\tr\times\vec E} \def\dcb{\vec\tr\times\vec B} \def\wz{\omega_0} \def\ef{\vec E} \def\ato{{A_{21}}} \def\bto{{B_{21}}} \def\bot{{B_{12}}} \def\bfieldTemplate:\vec B \def\apTemplate:A^\prime \def\xp{{x^{\prime}}} \def\yp{{y^{\prime}}} \def\zp{{z^{\prime}}} \def\tp{{t^{\prime}}} \def\upxTemplate:U x^\prime \def\upyTemplate:U y^\prime \def\e#1{\cdot10^{#1}} \def\eikrwt{e^{i(\vec k\vec r-wt)}} \def\qscat{Q_{scat}} \def\qabs{Q_{abs}}

\usepackage{fullpage} \usepackage{amsmath} \usepackage{eufrak} \begin{document} \def\lya{Ly\alpha}

\section{Random Walks}

If $\vec\phi=\phi_1,\phi_2,\dots$ is a random variable consisting of a series of random values, then a random walk $\vec w$ is a sum over this random variable: \begin{equation} w_i=\sum_{n=1}^{i}\phi_n \end{equation}

Random walks have the property that \begin{equation} |w_n|\propto\sqrt{n}, \end{equation} or more generally: \begin{equation} |w_n-w_m|\propto\sqrt{n-m} \end{equation}

\end{document} <\latex>