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Results tagged with open-problems
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user 238
If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
7
votes
The shortest path in first passage percolation
Gil, as you said, this is one of those typical FPP problems which seems obvious but is hard to prove. What have you tried already? It'd be helpful to know of some naïve attempts which didn't work.
…
- 8,532
4
votes
Open problems in PDEs, dynamical systems, mathematical physics
Percolation is a major outstanding research area in both theoretical and applied probability. I recommend reading the recent survey Percolation Since St. Flour by Geoffrey Grimmett and Harry Kesten (J …
4
votes
The shortest path in first passage percolation
Gil, thanks for bumping this post. I think I've got a new idea for you, but it's not a proof yet. Let $\gamma_n$ be a minimizing geodesic between $(-n,0)$ and $(n,0)$, and let $\gamma^{\pm}_n$ be a …
- 8,532
0
votes
distance regular metric spaces
Consider the unit sphere. Then p(π, π/2, π/2) = ∞. The north and south poles are distance π apart, and every point on the equator is distance π/2 from them.
Forcing every positive real distance to …
- 8,532