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Results tagged with discrete-geometry
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user 238
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
0
votes
3
answers
499
views
The symmetry group of $\mathbb Z^d$
Let $d \ge 1$, and consider the integer lattice $\mathbb Z^d$. This is a homogeneous space, in the manner of the Erlangan Programm.
I would like to write $\mathbb Z^d = G / H$, where $G$ is the symm …
- 8,532
5
votes
Shortest grid-graph paths with random diagonal shortcuts
I think this should be equivalent to a directed, site first-passage percolation (FPP) model where each site takes a passage time of $1$ or $\sqrt{2}$, each with probability $1/2$. I'm not convinced o …
- 8,532
8
votes
Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance Part II
By Donsker's theorem, this should converge to a Brownian motion in the scaling limit. This means that the shapes Robby McKilliam plotted will converge to a circle (when properly scaled), since the di …
- 8,532