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Fynn13
  • Member for 3 years, 2 months
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square matrix depending on complex value: spectral radius continous?
Okey, I'm a little confused. So in my case (the spectral radius), the counter examples above are correct or your text below?
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square matrix depending on complex value: spectral radius continous?
I don’t understand the difference. I am interested in the spectral radius of $A(z)$, that is the maximum of the absolute values of its eigenvalues.
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square matrix depending on complex value: spectral radius continous?
Thank you. Your examples are diagonal matrices: What if we would take just positive matrices? Lets say $A(z)\geq 0$.
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square matrix depending on complex value: spectral radius continous?
Thank you for the example, i will check that. Is the assertion true if we would take real values instead of complex?
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square matrix depending on complex value: spectral radius continous?
Sorry, I updated the answers to your questions!
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cemetery tree $\delta$
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Galton-Watson process: branching property
Do you maybe know where i can find the formalised definition of your comment?
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Galton-Watson process: branching property
I don’t see on Wikipedia the definition of the branching property.
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Random walks on GW-trees (regeneration epochs/survival set)
Can we therefore say: For a bias $\lambda<m$ holds $\mathcal{S}\subseteq \{ \Gamma_0<\infty\}$ because of infinitely many regeneration epochs and $ \{ \Gamma_0<\infty\}\subseteq \mathcal{S}$ because in the case $\Gamma_0<\infty$ the tree must be infinite?