Talk:Brownian tree

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Needs more careful definition

The present description omits two important details:

The particle is described as moved until it bumps into the seed. I infer that this is not actually what happens, as the tree would only result if the subsequent particles are moved, not until they bump into the original seed, but until they bump into any part of the (growing) tree.
In any case, the first particle will never bump into the seed! At least not if the seed is a point in the plane. It needs to have a finite size (such as being a small circle) in order to have any chance of having a particle bump into it. Either that, or the particle must be of finite size (or both). Having the seed be of finite size is probably best, to avoid the last piece of a branch before it connects to the tree be a smooth line segment.

I have no experience with these Brownian trees (though I work on evolutionary models that involve trees and Brownian Motion). So I have not tried to edit this page. Felsenst (talk) 12:56, 6 November 2010 (UTC)[reply]

Now the definition is improved a little, but still wrong. It says each particle is moved until it bumps into the original seed, or into any previous particle. No, it has to move until it bumps into any part of the tree. Not just into the final location of a previous particle. Felsenst (talk) 21:40, 24 June 2012 (UTC)[reply]

"Brownian trees are mathematical models of dendritic structures associated with the physical process known as _________" This is wrong - it's known as dendritic growth (actually). The physical process of dendritic growth (versus faceted growth) relies on other, material-specific issues, and is not determined by the distinction of "diffusion-limited" processes.

Generating a fractal or random walk pattern makes dendritic-looking structures, but this does not make it a physical model of dendritic growth, which requires materials specific distinctions (like heat and entropy of fusion) to differentiate the growth mode. Wikibearwithme (talk) 03:03, 27 October 2015 (UTC)Wikibearwithme (talk) 03:02, 27 October 2015 (UTC)[reply]

Wikibearwithme (talk) 02:54, 27 October 2015 (UTC)[reply]

Unclear

In the section Finite-dimensional laws

1) It says A tree is then defined by its shape (which is to say the order of the nodes).... The shape is not just the order of the nodes, whatever that might mean by itself. It must also be the topology, up to equivalence. I guess.

2) a probability law This appears to be an unnormalized probability measure.

2A02:1210:2642:4A00:4DF:8368:7F16:87DF (talk) 23:13, 18 June 2023 (UTC)[reply]

3) Suppose the sub-tree of $X$ generated by $k$ points, chosen randomly under $\mu$ ... Points or leaves? And what is

\mu

?

2A02:1210:2642:4A00:5470:3B10:B2D2:D156 (talk) 12:50, 20 June 2023 (UTC)[reply]