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Expanders. Sparse D-regular graphs that Have a short diameter Small cuts Large spectral gap Short mixing time. Salil’s slide. Spectral gap. D-regular graph – largest eigenvalue is D. Lmabdabar – second larget eigenvalue. Spectral gap:. History. Zig-Zag.
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Expanders Sparse D-regular graphs that • Have a short diameter • Small cuts • Large spectral gap • Short mixing time
Spectral gap • D-regular graph – largest eigenvalue is D. • Lmabdabar – second larget eigenvalue. • Spectral gap:
Zig-Zag Original motivation: a combinatorial construction with combinatorial proof for an important combinatorial object. Later byproducts: • First explicit construction of graphs with expansion above D/2. • SL=L.
Our goal • A zigzag variant with close to optimal spectral gap. • BL.