What is...random graph theory?
Вставка
- Опубліковано 12 вер 2024
- Goal.
I would like to tell you a bit about my favorite subfields of mathematics (in no particular order), highlighting key theorems, ideas or concepts and why I like them so much. This is a variation of “My favorite theorems” and I park the videos on that list as well.
This time.
What is...random graph theory? Or: Subfields of mathematics 5.
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.
Picture created using the below Mathematica code
Main discussion.
www.cambridge....
en.wikipedia.o...
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Background material.
en.wikipedia.o...)
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Computer talk.
doc.sagemath.o...
reference.wolf...
reference.wolf...
demonstrations...
Pictures used.
Picture from www.dtubbenhau...
Another picture from www.dtubbenhau...
Yet another picture from www.dtubbenhau...
Pictures created using the above Mathematica code
A final picture from www.dtubbenhau...
UA-cam and co.
• This random graph fact...
• Lecture 3. Random graphs.
• Random & Distributed G...
• Class 09: Erdos-Renyi ...
• What is...the Rado graph? (shameful self-promotion)
#graphtheory
#probabilitytheory
#mathematics
I hope you like random matrix theory as much - that intersects with my day job as an RNG designer.
I do like random matrix theory 🙂 I hope I can make a video about it at one point as well 😀
Wooow, If I hear randomness, I always remember percolations.
Interesting, see other comment.
Your videos would benefit from a higher quality microphone
Thanks for the feedback. I will see what I can do.
Next time: random sheafs on graphs. Ha!
Haha, yes, that sounds exciting 🤣
Ooff, is this actually percolation theory in disguise?
Ah, that sounds related, yes. I am not an expert about perculations, so someone help me out here please 🙂 I am curious, thanks for bringing this up.
@@VisualMath The percolation graph is very similar to the Random Graph G_np, but not all edges have a chance to be connected. Imagine a lattice of vertices. You can only connect those vertices who are immediately adjacent to each other. So, in the best case scenario, you will create a grid. You set the probability of connecting an edge just like in the Random Graph. Then you take note on whether the Percolation Graph is fully connected. If your probability of connection is between 0 and 0.5, you get a disconnected graph. From 0.5 to 1, the probability of the Percolation Graph being connected increases until it reaches 1 at probability of connection equal to 1.
@@VisualMath There's a great vid about Percolation Theory. I really like that one. I think that Percolation Theory is a subset of Random Graph Theory.
@@jakeaustria5445 Thanks, I will have a look.
@@jakeaustria5445 Thanks.