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Status: Unchecked ×Keyword: functional equations ×Clear all

1 claim from 1 paper

1. Computer Science › Constraint Satisfaction and Optimization

   The Asymptotics of the Clustering Transition for Random Constraint Satisfaction Problems

   Budzynski and Semerjian · Journal of Statistical Physics · 2020

   The paper locates the clustering transition of random hypergraph bicoloring and random graph colouring at large k and q, finding one shared constant and relating it to the rigidity threshold.

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   1. UncheckedThe paper characterises a constant γ_d by a functional equation, estimates it numerically at about 0.871, and derives an analytic lower bound of about 0.812.“We characterize $γ_{\rm d}$ via a functional equation, solve the latter numerically to estimate $γ_{\rm d} \approx 0.871$, and obtain an analytic lowerbound $γ_{\rm d} \ge 1 + \ln (2 (\sqrt{2}-1)) \approx 0.812$.”