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Keyword: condensation transition ×Clear all

3 claims from 1 paper

1. Computer Science › Constraint Satisfaction and Optimization

   The condensation transition in random hypergraph 2-coloring

   Coja‐Oghlan and Zdeborová · ACM-SIAM Symposium on Discrete Algorithms (SODA) · 2012

   The paper proves a condensation transition exists in random hypergraph 2-colouring, finds the second moment method fails before it, and slightly improves bounds on the colourability threshold.

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   1. UncheckedThe paper proves that a condensation phase transition occurs in random hypergraph 2-colouring, a natural random constraint satisfaction problem.“In this paper we prove for the first time that a condensation transition exists in a natural random CSP, namely in random hypergraph 2-coloring.”
   2. UncheckedIn random hypergraph 2-colouring, the second moment method stops working strictly earlier than the condensation transition occurs.“Perhaps surprisingly, we find that the second moment method breaks down strictly \emph{before} the condensation transition.”
   3. UncheckedThe authors' proof of a condensation transition also gives slightly improved bounds on the threshold for random hypergraph 2-colourability.“Our proof also yields slightly improved bounds on the threshold for random hypergraph 2-colorability.”