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Results tagged with laplacian
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user 18974
The Laplacian matrix is the representation of a graph in matrix form.
7
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0
answers
385
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Sequence of graphs with small $\lambda_1$ (the smallest nonzero eigenvalue of a regular fini...
The combinatorial laplacian on a finite graph $G$ can be defined as $ \Delta: \mathbb{C}^G \to \mathbb{C}^G$ sending the function $f:G \to \mathbb{C}$ to $(\Delta f)(v) = \sum_{v' \sim v} \big( f(v)-f( …
- 4,432
4
votes
2
answers
543
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How does a quasi-isometry affect Poisson or Martin boundaries?
Take two graphs (of bounded valency) or manifolds (f bounded geometry) $G$ and $G'$. Assume there is a quasi-isometry $f:G \to G'$, and assume the Poisson or Martin boundary of $G$ is known, what may …
- 4,432
1
vote
0
answers
232
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Lp norm estimates for the inverse of the Laplacian on a graph
I am looking at a finite connected graph and I would like to know what is the best [i.e. largest] constant $\lambda_p$ in
$$
\sum_x f(x) =0 \implies \| \Delta^{-1} f\|_{\ell^p} \leq \lambda_p^{-1} \| …
- 4,432