The random-cluster model has a uniqueness transition at p_s(q,Δ) on wired Δ-regular trees for all q, yielding near-linear mixing of Glauber dynamics on trees and on random regular graphs when q ≥ C log Δ.
Martinelli
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Uniqueness and Mixing in the Low-Temperature Random-Cluster Model on Trees and Random Graphs
The random-cluster model has a uniqueness transition at p_s(q,Δ) on wired Δ-regular trees for all q, yielding near-linear mixing of Glauber dynamics on trees and on random regular graphs when q ≥ C log Δ.
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Glauber dynamics for random field Ising models on bounded degree graphs and MLSI
Glauber dynamics for RFIM on bounded-degree graphs mixes in polynomial time w.h.p. under anti-concentrated random fields, with MLSI and weak Poincaré inequalities also established.
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Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful
Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.