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Expanders

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

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  1. Expanders Sparse D-regular graphs that • Have a short diameter • Small cuts • Large spectral gap • Short mixing time

  2. Salil’s slide

  3. Spectral gap • D-regular graph – largest eigenvalue is D. • Lmabdabar – second larget eigenvalue. • Spectral gap:

  4. History

  5. 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.

  6. Our goal • A zigzag variant with close to optimal spectral gap. • BL.

  7. Zig-zag product

  8. Iterative construction.

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