618 reputation
117
bio website http://-
location Sweden
age 25
visits member for 1 year, 9 months
seen 2 days ago

I'm currently a Ph.D. student in probability theory at Chalmers University of Technology in Gothenburg, Sweden.


Jul
2
awarded  Curious
Apr
23
comment Can a cube always be fitted into the projection of a cube?
It should be centered around the origin. I edited the question so that this is clear.
Apr
23
revised Can a cube always be fitted into the projection of a cube?
Added a restriction
Apr
21
comment Can a cube always be fitted into the projection of a cube?
Only orthogonal I think
Apr
20
awarded  Nice Question
Apr
15
comment Is the eigenvectors of vertex transitive graphs bounded
Given that $\| \psi \|_2^2=|S|$, it is obvious that $\| \psi \|_\infty<\sqrt{|S|}$ for any such $\psi$.
Apr
15
awarded  Promoter
Apr
14
revised Does any vertex transitive graph have a bounded eigenvector?
Changed the question slightly to make it more restrictive, and hopefully easier to answer
Apr
12
comment Does any vertex transitive graph have a bounded eigenvector?
@user126154, the property you describe is irreducibility of the random walk/Markov chain, this is NOT the same as vertex transitivity. See here: en.wikipedia.org/wiki/Vertex-transitive_graph
Apr
11
comment Number of Nodes within a Given Distance from a Node
The book "Spectral Graph theory" by Fan Chung (the first chapters are avaiable online through her homepage) contains some such bounds, e.g. $\max_{i \not = 1} |\lambda_i| \geq \sqrt{\frac{n-d}{(n-1)d}}$.
Apr
11
revised Does any vertex transitive graph have a bounded eigenvector?
edited title
Apr
11
comment Does any vertex transitive graph have a bounded eigenvector?
@user126154, I do not understand why any of the two examples you suggested should be vertex transitive?
Apr
11
revised Does any vertex transitive graph have a bounded eigenvector?
Added some motivation
Apr
11
asked Does any vertex transitive graph have a bounded eigenvector?
Apr
11
accepted Is the eigenvectors of vertex transitive graphs bounded
Apr
11
comment Is the eigenvectors of vertex transitive graphs bounded
This is not really what I needed, but rather that there will always exist at least one eigenvector $\phi'$ in the same eigenspace as $\phi$ for which the mentioned property holds, i.e. that $\| \phi' \|_\infty < C$ for some constant $C$ which does not depend on the graph. This seems to be true on at least some quite simple graphs, such as the the circle and the hypercube. The stronger property described in the question would imply this property, why it seemed reasonable to investigate this first.
Apr
10
asked Can a cube always be fitted into the projection of a cube?
Apr
10
revised Is the eigenvectors of vertex transitive graphs bounded
Fixed a LaTeX error
Apr
10
asked Is the eigenvectors of vertex transitive graphs bounded
Jan
16
accepted Difference between two inequality symbols