Graduate student in physics at UIUC

Apr
29
awarded Popular Question
Apr
27
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
26
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
26
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
26
comment How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
Then let me check again!
Apr
26
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
26
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Apr
26
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
25
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?
Apr
25
comment Is anything known about the eigenspectrum of the regular representation of the permutation group?
If the eugenvalues are so trivial then what is Stembridge calculating?
Apr
25
comment Is anything known about the eigenspectrum of the regular representation of the permutation group?
I am missing something here. Why are the character formulas so much more difficult for this permutation group if the eigenvalues are so trivial?
Apr
16
comment Special properties of bipartite expanders
@SashoNikolov Actually the MSS proof doesn't even need the parity symmetric nature. Thats why I said that the proof is little more general than that. All that they need is that the spectral radius of the graph is upper bounded by the largest eigenvalue. It just so happens that for bipartite graphs this condition is true.
Apr
16
revised Special properties of bipartite expanders
added 169 characters in body
Apr
13
answered Special properties of bipartite expanders
Apr
11
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10
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10
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10
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