Timeline for Particles sent into the same direction with uniformly distributed speed
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2022 at 13:17 | comment | added | Michael Engelhardt | @AnthonyQuas - I am interested in why our intuitions are so different. My intuition is that the probability that some particle survives is one ... for a start, the probability that the first particle has speed $n$ is $1/n$, and it will survive, so that's a (bad) lower bound for the probability. For $n=2$, the problem is equivalent to a one-dimensional unbiased random walk, where nothing surviving means the random walk never revisits the origin - I think the probability of that is zero? And from that, I extrapolate to any $n$ (ha ha). | |
| Sep 14, 2022 at 12:53 | comment | added | James Martin | Also related (bullets with continuous speeds): "The combinatorics of the colliding bullets" by Broutin and Marckert: doi.org/10.1002/rsa.20869 (and its references and citations). | |
| Sep 14, 2022 at 12:49 | comment | added | aorq | Brittany Dygert, Christoph Kinzel, Matthew Junge, Annie Raymond, Erik Slivken. Jennifer Zhu. "The bullet problem with discrete speeds." Electronic Communications in Probability 24 1--11, 2019. doi.org/10.1214/19-ECP238 scholarworks.umass.edu/cgi/… | |
| Sep 14, 2022 at 12:08 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
edited to address questions for clarification in comment section
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| Sep 14, 2022 at 12:04 | comment | added | Dominic van der Zypen | Thanks for your questions for clarification - I will edit the original post so that the questions are answered. | |
| Sep 14, 2022 at 11:30 | comment | added | Dieter Kadelka | And to simplify particles with speed $0$ can be omitted. They all get annihilted at position 0. As a consequence speed should be chosen uniformly in $\{1,\ldots,n\}$. | |
| Sep 14, 2022 at 9:42 | comment | added | Anthony Quas | What if a particle is released at time 0 traveling at speed 1; and a new particle is released at time 1, traveling at speed 10. Do they “collide” between time 1 and time 2 or do they not collide because they never occupy the same site at the same (integer) time. If the former, I think it should be pretty easy to show that almost surely nothing survives. If the latter, I think the answer should be the same, but the proof may be a bit more involved. | |
| Sep 14, 2022 at 8:01 | comment | added | LeechLattice | What if three or more particles collide at the same time? | |
| Sep 14, 2022 at 6:34 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |