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Keyword: variational principle ×Clear all

2 claims from 1 paper

1. Physics and Astronomy › Theoretical and Computational Physics

   Reconstruction on Trees and Spin Glass Transition

   Mézard and A · Journal of Statistical Physics · 2006

   The paper links reconstructing a symbol broadcast through a noisy tree to a glass transition in physics, then derives new rigorous bounds on the reconstruction threshold, including for antiferromagnetic Potts channels.

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   1. UncheckedThe noise level below which a symbol sent through a tree can be recovered coincides with a glass transition in a related statistical physics problem.“We show that this threshold coincides with the dynamical (replica symmetry breaking) glass transition for an associated statistical physics problem.”
   2. UncheckedThe authors prove a bound on reconstruction for antiferromagnetic Potts channels, giving new results on random proper colourings of infinite regular trees.“In particular, we prove a bound on the reconstruction problem for the antiferromagnetic ``Potts'' channels, which implies, in the noiseless limit, new results on random proper colorings of infinite regular trees.”