Timeline for Random walk by simplex vertices
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 31, 2013 at 21:27 | history | edited | Dylan Pizzo | CC BY-SA 3.0 |
added 69 characters in body
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| Dec 31, 2013 at 20:34 | history | edited | Dylan Pizzo | CC BY-SA 3.0 |
added 672 characters in body; deleted 663 characters in body
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| Dec 16, 2013 at 16:10 | history | edited | Dylan Pizzo |
Added closed-form tag
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| Dec 15, 2013 at 22:11 | answer | added | ofer zeitouni | timeline score: 4 | |
| Dec 15, 2013 at 13:09 | history | edited | Dylan Pizzo | CC BY-SA 3.0 |
fixed that the lower bound should be for r=2 instead of r=3.
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| Dec 15, 2013 at 12:57 | comment | added | Dylan Pizzo | @oferzeitouni Actually, Ben Barber's answer below contains an illustration of the r=2 case. | |
| Dec 15, 2013 at 11:50 | answer | added | Ben Barber | timeline score: 3 | |
| Dec 15, 2013 at 11:48 | comment | added | ofer zeitouni | I'm still having troubles following what you mean. Can you describe it for r=2? | |
| Dec 15, 2013 at 10:56 | history | edited | Dylan Pizzo | CC BY-SA 3.0 |
changed simplex to regular simplex.
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| Dec 15, 2013 at 10:49 | comment | added | Dylan Pizzo | @ofer When you say $Z^r$, do you mean $\mathbb{Z}^r$? If you do, then no. At every point, the bug has exactly $r+1$ choices of direction, which are the vertices of a regular simplex (link) at which the bug is centered. The simplices must also all be oriented in the same direction. Also, in the second question, the digits don't have to appear in order; there simply has to be a point such that the number of occurences of the digit $n$ is equal for all $0\le n\le b$. Does that make sense? | |
| Dec 15, 2013 at 7:19 | comment | added | ofer zeitouni | Do I understand correctly that your bug is simply performing a simple random walk on the lattice $Z^r$? I do not quite see the equivalence of the questions (why do you need all digits to appear in order to return to the origin). Can you clarify? | |
| Dec 15, 2013 at 1:15 | history | asked | Dylan Pizzo | CC BY-SA 3.0 |