Calculating diffusion coefficient from jump statistics

First published:

Last Edited:

Number of edits:

If we have a random process, such as when looking at Brownian Motion, we can look at the individual displacements $\Delta x$, and we'll get[@catipovic2013Improving the quantification of Brownian motion]

$$\textrm{Var}(\Delta x) = \left< \Delta x^2\right> - \left<\Delta x\right>^2$$

For standard Brownian processes, we also have $\left<\Delta x\right> = 0$

And from here, we have that the variance is equal to the mean-squared displacement, which can be re-written as the known equation:

$$\left<\Delta x^2\right> = 2Dt$$

In this case $t$ is the time between frames in the measurement (which is given as constant).


Share your thoughts on this note
Aquiles Carattino
Aquiles Carattino
This note you are reading is part of my digital garden. Follow the links to learn more, and remember that these notes evolve over time. After all, this website is not a blog.
© 2021 Aquiles Carattino
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
Privacy Policy