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.
Entropic independence I : Modified log- S obolev inequalities for fractionally log-concave distributions and high-temperature I sing models
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Sparse localization deduces entropic independence from sparse ℓ2-independence with explicit loss, yielding approximate entropy conservation for uniform independent sets of fixed size in bounded-degree graphs.
Proves polynomial mixing of Glauber dynamics at the antiferromagnetic two-spin uniqueness threshold and optimal logarithmic mixing for Swendsen-Wang dynamics on bounded-degree graphs, resolving a conjecture.
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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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Entropic independence via sparse localization
Sparse localization deduces entropic independence from sparse ℓ2-independence with explicit loss, yielding approximate entropy conservation for uniform independent sets of fixed size in bounded-degree graphs.
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Edge-Tilting Field Dynamics: Rapid Mixing at the Uniqueness Threshold and Optimal Mixing for Swendsen-Wang Dynamics
Proves polynomial mixing of Glauber dynamics at the antiferromagnetic two-spin uniqueness threshold and optimal logarithmic mixing for Swendsen-Wang dynamics on bounded-degree graphs, resolving a conjecture.