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What is...the drunken bird constant? 

VisualMath
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Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...the drunken bird constant? Or: Coming home, or not…?
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
www.dtubbenhaue...
TeX files for the presentation.
github.com/dtu...
Thumbnail.
Main discussion.
Section 5.9 from vignette.wikia... (this is Mathematical Constants - S.R. Finch)
mathworld.wolf...
Background material.
www.ime.unicam...
en.wikipedia.o...
math.stackexch...
math.stackexch...
en.wikipedia.o...
people.duke.ed...
mathworld.wolf...
/ random-walk-a-comprehe...
blogs.sas.com/...
mathstrek.blog...
/ the-drunkards-walk-exp...
mathworld.wolf...
www.bragitoff....
math.stackexch...
mathoverflow.n...
• Visualizing Random Wal...
Computer talk.
demonstrations...
demonstrations...
demonstrations...
demonstrations...
demonstrations...
Pictures used.
Picture created using reference.wolf...
A variation of mathematica.st...
Another variation of the same wonderful post
i.pinimg.com/o...
Picture created using reference.wolf...
RU-vid and co.
• What is a Random Walk?...
• Why Do Random Walks Ge...
#combinatorics
#dynamics
#mathematics

Опубликовано:

 

14 окт 2024

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Комментарии : 2   
@peabrainiac6370
@peabrainiac6370 5 месяцев назад
When looking at the graph near the end of the video, it would've also been interesting to see how close this probability gets to the trivial lower bound of 1/(2d) for larger d - intuitively I'd expect it to get rather close, but with how complicated the integral formula is it's quite cumbersome to try plotting it myself. Nonetheless a neat video though of course ^^'
@VisualMath
@VisualMath 5 месяцев назад
Interesting question, I don’t know but I would bet that this is known. In any case, I plotted the first 50 integrals versus 1/(2d) and they seem to get arbitrary close. I would guess that they are asymptotically the same for dimension → infinity 🤔