For every feasible margins on an m imes n binary matrix the lazy swap chain has spectral gap at least binom(m,2)^{-1} binom(n,2)^{-1}, which is tight.
Coupling from the past
10 Pith papers cite this work, alongside 718 external citations. Polarity classification is still indexing.
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718
external citations · OpenAlex
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Establishes variance lower bounds for hitting times of random walks on graphs and disproves a conjecture on local nonconcentration via high-degree constructions.
For any fixed β, there exists a system-size-independent external field θ such that Glauber dynamics on the SK model mixes in polynomial time with high probability.
Defines temporal conductance Φ for dynamic networks and proves the voter model consensus time is O(m/(d_min Φ)) with a tight lower bound.
Tempering chains achieve polynomial spectral gap lower bounds of order 11-12 for multimodal Gibbs measures without explicit energy landscape structure.
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
EntroPath defines a free-energy dissimilarity from maximum-entropy random walk path ensembles and proves it converges to squared geodesic distance in the short-time limit via Varadhan's formula.
A genus-preserving chord swap Markov chain on chord diagrams is shown to mix in polynomial time for any fixed genus.
Establishes weak convergence of the quadratic field for speed-change Kawasaki dynamics to equilibrium fluctuation in the non-gradient case.
Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.
citing papers explorer
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Spectral Gap for the Binary Fixed-Margin Swap Chain
For every feasible margins on an m imes n binary matrix the lazy swap chain has spectral gap at least binom(m,2)^{-1} binom(n,2)^{-1}, which is tight.
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Nonconcentration of hitting times for random walks on graphs
Establishes variance lower bounds for hitting times of random walks on graphs and disproves a conjecture on local nonconcentration via high-degree constructions.
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Mixing of Glauber Dynamics on High Overlap Gibbs Measures
For any fixed β, there exists a system-size-independent external field θ such that Glauber dynamics on the SK model mixes in polynomial time with high probability.
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Temporal Conductance and Bounds on the Voter Model for Dynamic Networks
Defines temporal conductance Φ for dynamic networks and proves the voter model consensus time is O(m/(d_min Φ)) with a tight lower bound.
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Rapid convergence of tempering chains to multimodal Gibbs measures
Tempering chains achieve polynomial spectral gap lower bounds of order 11-12 for multimodal Gibbs measures without explicit energy landscape structure.
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Cutoff for mixtures of permuted Markov chains: reversible case
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
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EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning
EntroPath defines a free-energy dissimilarity from maximum-entropy random walk path ensembles and proves it converges to squared geodesic distance in the short-time limit via Varadhan's formula.
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Polynomial mixing for polygonal side matchings
A genus-preserving chord swap Markov chain on chord diagrams is shown to mix in polynomial time for any fixed genus.
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Quadratic fluctuations of speed-change Kawasaki dynamics
Establishes weak convergence of the quadratic field for speed-change Kawasaki dynamics to equilibrium fluctuation in the non-gradient case.
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Quantum graph models of quantum chaos: an introduction and some recent applications
Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.