Proves spectral gap lower bound of binom(m,2)^{-1} binom(n,2)^{-1} for the lazy swap chain on m by n binary matrices with arbitrary feasible margins, resolving the Kannan-Tetali-Vempala conjecture.
Coupling from the past
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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.
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.
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.
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Spectral Gap for the Binary Fixed-Margin Swap Chain
Proves spectral gap lower bound of binom(m,2)^{-1} binom(n,2)^{-1} for the lazy swap chain on m by n binary matrices with arbitrary feasible margins, resolving the Kannan-Tetali-Vempala conjecture.
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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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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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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.