Graduate student in physics at UIUC

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revised What do we know about checking real-stability of multivariate complex polynomials?
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May
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revised What do we know about checking real-stability of multivariate complex polynomials?
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revised What do we know about checking real-stability of multivariate complex polynomials?
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revised What do we know about checking real-stability of multivariate complex polynomials?
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comment Characterization of an irreducible matrix
Some other discussions which might be helpful : (1) math.stackexchange.com/questions/750817/… (2) math.stackexchange.com/questions/315453/…
May
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revised What do we know about checking real-stability of multivariate complex polynomials?
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May
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asked What do we know about checking real-stability of multivariate complex polynomials?
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awarded Popular Question
Apr
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comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
@Asaf Looking at that Terence Tao's article it seems that they cannot guarantee any good spectral gap from the property of quasirandomness. Is that right?
Apr
27
asked How does one calculate/estimate/guarantee the girth of a non-Abelian Cayley graph?
Apr
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comment About expectation norms on graphs
Appendix B, page 63 of this paper seems to use these without any proof or reference arxiv.org/pdf/1205.4484v3.pdf
Apr
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comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
^Can you give a reference to this? It seems very hard to find examples of such girth calculation for Cayley graphs!
Apr
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comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
Then let me check again!
Apr
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comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
Yes. I know that. But its not clear to me that this LPS paper actually proves this logarithmic girth property. They take a totally eigenvalue approach to get their sharp numbers. I am looking for techniques to prove high girth. Let me put up a separate question about it.
Apr
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awarded Investor
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comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
Is there any reference for the proof of this property for SL_2(F_p) ? Any reference for techniques about proving lower bounds or calculating the girth of non-Abelian Cayley graphs?
Apr
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comment Is anything known about the eigenspectrum of the regular representation of the permutation group?
^Isn't the argument of ARupinsky more generic? g^(its order) = e and hence in any representation the matrix of g will have the characteristic equation x^(its order) = 1 and then all the eigenvalues become roots of unity? What am I missing?
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