Timeline for Random walk is to diffusion as self-avoiding random walk is to ...?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2023 at 17:27 | history | edited | Harry Richman | CC BY-SA 4.0 |
fix wikipedia link
|
| Aug 1, 2011 at 19:23 | comment | added | Ron Maimon | There is no direct analog because for ordinary random walk, you don't need to know the past to go forward in time. To go forward in time in a self-avoiding walk, you need to know the past, so you know what to avoid. This means that there is no differential equation form of the process, which is what I think you wanted. | |
| Jul 3, 2010 at 13:07 | vote | accept | Joseph O'Rourke | ||
| Jul 3, 2010 at 13:07 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
added 380 characters in body
|
| Jul 2, 2010 at 13:17 | comment | added | Joseph O'Rourke | @jc: Thanks for the connection. I can see that many of the references in the Lawler paper to which Yuri pointed me are to journals such as J. Statist. Phys., J. Stat. Mech. Theory Exp., J. Math Phys., Phys. Let., etc. I may be in over my head, but it should be a fun swim! | |
| Jul 2, 2010 at 13:05 | comment | added | j.c. | This might be off-topic for this site, but you may also want to look at polymer physics books to see how physicists treat problems involving lots of long chains of molecules. (Surprisingly often, self-avoidance turns out to be unimportant to the properties of polymeric materials.) There's an article by Tom McLeish in a recent Physics Today that serves as a teaser to the field dx.doi.org/10.1063/1.2970211 (it may be easier to find if you go to your institution's physics library and browse through recent issues), and a good introductory book is Introduction to Polymer Physics by Doi. | |
| Jul 2, 2010 at 12:31 | answer | added | PeterR | timeline score: 3 | |
| Jul 2, 2010 at 12:03 | answer | added | Yuri Bakhtin | timeline score: 15 | |
| Jul 2, 2010 at 12:01 | comment | added | Joseph O'Rourke | @Tom Boardman: Yes, that work of Sumners and Whittington on random knots is fascinating! Whether knot theory is analogous to diffusion in this situation is not clear to me. I am seeking a continuous theory that parallels and informs the discrete. | |
| Jul 2, 2010 at 10:36 | comment | added | Tom Boardman | See this old blog post: maa.org/mathland/mathtrek_11_3.html for a very gentle introduction. This is about the extent of my knowledge though... | |
| Jul 2, 2010 at 10:31 | comment | added | Tom Boardman | Random knots :) | |
| Jul 2, 2010 at 10:21 | history | asked | Joseph O'Rourke | CC BY-SA 2.5 |