Timeline for How far can a particle travel from its origin if it exhibits self-avoiding Brownian motion in two-dimensions?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 8, 2017 at 10:41 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Jul 31, 2011 at 4:28 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Addendum on mean path length.
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| Jul 31, 2011 at 0:31 | comment | added | Ron Maimon | I assumed when I did the simulation (many years ago, and I no longer have the code) that the number of self avoiding walks of length N should be 4^N times exp(-S), that is, the number of walks reduced by the probability cost of self avoidance. This gave the wrong answer, and at the time, I convinced myself that this was due to some measure subtlety, but I forget what. | |
| Jul 30, 2011 at 23:43 | comment | added | Ron Maimon | A better way to do the simulation is as follows: simulate the path, whenever the path closes a loop, there are always extensions which are outside (lattice connected to infinity), but there might be extensions which are inside too. Whenever you reach such a point, use an inside/outside algorithm (draw an irrational line and count the parity of the number of intersections with the curve) to add a factor of log(number of inside points)-log(number of neighbors) to a variable S. The variable S is eventually linear, and it is the log of the asymptotic fraction of RWs which are not trapped per step. | |
| Jul 30, 2011 at 15:56 | vote | accept | Rob Grey | ||
| Jul 30, 2011 at 15:01 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |