Probably because square grid is topologicaly noncompact and that it requires boundary conditions to be specified while setup on torus is topologycaly compact and does not require boundary conditions (reason why it's more generic than finite square grid).
when tf did my feed go from neo nazi shit to this. I fw it though, didn't know what a Laplacian was until now. Always hated graph theory back in Uni cus I thought it was shallow. I wonder why we weren't taught this stuff?
how could one predict whether the system will reach some equilibrium state or frustrated state?
Great talk. I wish I'd seen that motivation when I was studying this.
aleinunas kerp lipton lovasz rackoff RandomWalk 25:34
15:40
this might be the best explanation on spectral graph theory on the internet!
Great video! sparked some ideas
great watch, thanks
30:00
Can I ask what the protest was about?
From what I can gather, university students in Berkley, California were protesting the death of Eric Garner.
Can I get a citation for the proof mentioned in 32:30?
annals.math.princeton.edu/wp-content/uploads/annals-v175-n3-p08-s.pdf
awesome
what is the exact reason that the random walk was done on a torus and not on a square ?
A square with opposite edges identified is a torus.
Probably because square grid is topologicaly noncompact and that it requires boundary conditions to be specified while setup on torus is topologycaly compact and does not require boundary conditions (reason why it's more generic than finite square grid).
The grid on a torus is 4-regular.
Also note that the torus is topologically nontrivial ( genus-1 surface) which impacts the long term diffusion behaviour
Torii have the easiest boundary conditions to program probably (just have to write every coordinate modulo, no need to write any special cases).
when tf did my feed go from neo nazi shit to this. I fw it though, didn't know what a Laplacian was until now.
Always hated graph theory back in Uni cus I thought it was shallow. I wonder why we weren't taught this stuff?