Timeline for xkcd's "Unsolved Math Problems", straight lines in random walk patterns
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2021 at 3:28 | comment | added | bRost03 | @Keba if you get boxed in discard that walk and begin again. A better way to think of the question might be: consider ALL possible SAWs of NK steps with a marble placed at every Nth step. What is the average number of marbles on the longest line? | |
| Oct 18, 2021 at 20:31 | comment | added | LSpice | @ZachTeitler, re, a (literally) bold new notation for the $5$-adics? | |
| Oct 18, 2021 at 17:01 | comment | added | Zach Teitler | @Gro-Tsen It's a "conjection" whatever that is. (Also: I wonder what $\mathbb{5}$ is supposed to mean.) | |
| Oct 18, 2021 at 16:35 | comment | added | Will Sawin | @SamHopkins A horizontal or vertical line through the origin will have $\sqrt{K/N}$ marbles on average and I would wildly guess that the correct answer is within $(KN)^\epsilon$ of this. It looks conceivable to prove this by bounding for each line the expectation of the $\ell$th power of the number of marbles on the line and summing over all lines passing through at least a few points within a distance $NK$ of the origin. | |
| Oct 18, 2021 at 16:09 | comment | added | Sam Hopkins | If we consider the analogous process for a random walk which is not self-avoiding, is this understood? (SAWs are much harder than regular random walks, from what I understand…) | |
| Oct 18, 2021 at 16:08 | comment | added | markvs | @Gro-Tsen: $\epsilon$ cannot be $\lt 0$. | |
| Oct 18, 2021 at 16:00 | comment | added | LSpice | I believe deeplinking to images on XKCD is discouraged, so I changed the link to point to the comic. | |
| Oct 18, 2021 at 16:00 | history | edited | LSpice | CC BY-SA 4.0 |
Changed link to comic rather than deeplink to image
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| Oct 18, 2021 at 12:35 | comment | added | Gro-Tsen | What I very much want to know is: is the Euler field manifold hypergroup isomorphic to a Gödel-Klein meta-algebreic $\epsilon<0$ quasimonoid connection under Sondheim calculus? (Also, what in Apollo's name is going on with this curve?) | |
| Oct 18, 2021 at 12:19 | comment | added | Radost | @MartinHairer Is this 'dropping a marble' part redundant then? Is it roughly equivalent to how many collinear gridpoints were visited? | |
| Oct 18, 2021 at 9:44 | comment | added | Radost | @Keba either seems interesting but I think the original intention was point-like marbles. | |
| Oct 18, 2021 at 9:21 | comment | added | Martin Hairer | The self-avoiding random walk with $N$ steps is usually simply defined as the uniform measure on the set of all self-avoiding walks of $N$ steps. It doesn't have any kind of Markov property, but is conjectured in $2D$ to converge to an SLE curve with self-similarity exponent $3/4$. Rigorously, almost nothing non-trivial is known about its large-$N$ behaviour. | |
| Oct 18, 2021 at 9:20 | comment | added | Wojowu | I feel like we are getting nerd sniped again... | |
| Oct 18, 2021 at 9:02 | comment | added | Keba | Also, how large are these marbles? Do they fill the whole square? Are they just points? | |
| Oct 18, 2021 at 9:00 | comment | added | Keba | I'm no expert on random walks so I probably miss something easy, but why is this process well-defined? I might corner myself in? | |
| Oct 18, 2021 at 8:56 | history | edited | David Loeffler | CC BY-SA 4.0 |
fix link
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| Oct 18, 2021 at 8:56 | history | edited | Arno | CC BY-SA 4.0 |
fixed link (hopefully)
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| Oct 18, 2021 at 8:49 | history | asked | Radost | CC BY-SA 4.0 |