5 research outputs found
Explicit near-Ramanujan graphs of every degree
For every constant and , we give a deterministic
-time algorithm that outputs a -regular graph on
vertices that is -near-Ramanujan; i.e., its eigenvalues
are bounded in magnitude by (excluding the single
trivial eigenvalue of~).Comment: 26 page
The SDP Value for Random Two-Eigenvalue CSPs
We precisely determine the SDP value (equivalently, quantum value) of large
random instances of certain kinds of constraint satisfaction problems,
``two-eigenvalue 2CSPs''. We show this SDP value coincides with the spectral
relaxation value, possibly indicating a computational threshold. Our analysis
extends the previously resolved cases of random regular and
, and includes new cases such as random
(equivalently, ) and CSPs. Our techniques
include new generalizations of the nonbacktracking operator, the Ihara--Bass
Formula, and the Friedman/Bordenave proof of Alon's Conjecture.Comment: 50 pages excluding title page and table of content