Timeline for How to mathematically justify the "sampling" over only $100$ random matrices to estimate percolation thresholds?
Current License: CC BY-SA 4.0
10 events
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| Aug 19, 2018 at 21:56 | comment | added | user127888 | @CarloBeenakker I was reading the paper you linked but am a bit confused. How is occupation probability $p$ in a binary matrix related to the seed mass "SM"? Also, do you have some other references, apart from that paper which shows the $\Pi$ vs. $p$ graphs for different $L$'s? | |
| Aug 19, 2018 at 12:17 | comment | added | user127888 | @CarloBeenakker Thanks. That paper looks excellent! | |
| Aug 19, 2018 at 12:03 | comment | added | user127888 | @LSpice Well, it came up during an undergrad research project (which will probably be sent for publication), so I asked here. Also, I wanted to hear a professional mathematician's take on the question. Carlo already clarified a bit. In case other people here also feel that it should be migrated to SSE, I have no problem with that, of course. Feel free to flag for migration! :) | |
| Aug 19, 2018 at 11:55 | review | Close votes | |||
| Aug 20, 2018 at 20:03 | |||||
| Aug 19, 2018 at 11:39 | comment | added | LSpice | I think that this is a good and thoughtful question, but that it isn't about research-level mathematics, and so probably doesn't belong here. Maybe SSE? | |
| Aug 19, 2018 at 11:35 | comment | added | Carlo Beenakker | see for example figure 3 of this publication, which also shows you how these considerations are applied to real-world problems (the percolation of a single tree species in a forest). | |
| Aug 19, 2018 at 11:30 | comment | added | user127888 | @CarloBeenakker Thanks, that makes sense indeed. Unrelated: Do you happen to know any source which explicitly shows how the $\Pi$ vs $p$ graph varies for different $L$'s ? Stauffer doesn't have it. | |
| Aug 19, 2018 at 11:10 | comment | added | Carlo Beenakker | your concerns apply to any experiment, whether it is in the real world or on a computer; only in rare cases can statistical errors be bounded from mathematical considerations, and typically when that is possible the problem is not really interesting from the physics point of view; what you can do is compare results from 100 configurations with those from, say, 500 configurations; this can give you error bars on your findings, and those will give you confidence in your conclusions. | |
| Aug 19, 2018 at 10:11 | review | First posts | |||
| Aug 19, 2018 at 12:06 | |||||
| Aug 19, 2018 at 10:07 | history | asked | user127888 | CC BY-SA 4.0 |