Talk:Brownian motion

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Inertial effects in the Langevin equation[edit]

From the article: "Inertial effects have to be considered in the Langevin equation, otherwise the equation becomes singular.[clarification needed] so that simply removing the inertia term from this equation would not yield an exact description, but rather a singular behavior in which the particle doesn't move at all.[clarification needed]"

It seems to me that "removing the inertia term from this [Langevin] equation" leads to the equation $\lambda \mathbf {v} =\mathbf {\eta (t)}$ , implying $\mathbf {x} (t)=\int _{0}^{t}\mathbf {\eta (t)} dt$ (following https://en.wikipedia.org/wiki/Langevin_equation#Brownian_motion_as_a_prototype) Such an $x(t)$ should be a Gaussian distributed random variable: $x(t)\sim {\mathcal {N}}(0,t)$ , which is what we want. In this case, we could simply remove the text above. What do you think? I may be missing something simple... Spencerjpeters (talk) 05:17, 19 November 2019 (UTC)

Yeah that whole paragraph is problematic for a number of reasons. Unless someone else fixes it first, I will later when I have more time. MaxwellMolecule (talk) 05:21, 19 November 2019 (UTC)

The caption[edit]

The caption to the first picture says the variance is 2. What does that mean when we're talking about a vector-valued random variable, rather than scalar-valued? Often one speaks of a covariance matrix, or of a "variance" that is that matrix or is the associated linear transformation. Michael Hardy 23:42, 23 Jan 2005 (UTC)

Right, I changed the caption to make that clear. Paul Reiser 05:27, 24 Jan 2005 (UTC)

Central Limit theorem[edit]

I think that the mathematical section should make reference to the Central limit theorem, which explains (as far as I know) why the position of a particle at a time t can be considered as normally distributed random variable. Psychofox 01:37, Mar 21, 2005 (UTC)

Smoluchowski[edit]

It is absolutely necessary that Smoluchowski's contributions are discussed here. He worked jointly with Einstein, and derived formulae that are fundamental to the study of stochastic processes. The wikipedia article does not give much information on him, but there are a number of other sources.

Why not add to the wikipedia article using those sources? PAR 30 June 2005 17:35 (UTC) (PS - type four tildes to sign your name)

Excellent Communication of Subject[edit]

I would like to express my great gratitude and approval for the 'Intuative Metaphor' section in this article. I found it extremely useful in understanding more of this topic. As another commented, the subject is rather complicated, in nature and presentation. This somewhat oblique description really serves to facilitate intelligent reading, especially for mathematical laypersons.

I personally like Douglas Adams' example for brownian motion, e.g. a nice cup of hot tea.

πήδηση[edit]

πήδησις /pέ(ε)ːdε(ε)ːsis/ η = ε(ε) in ancient Greek, but /i/ in modern Greek (pedesis, modern: 'pidisis) ______

katharevousa: πέδηση, πέδησις = braking also pedesis is a different word (pedesis, modern: 'pedisis)

anhducwiki

Thursday, April 30, 2020