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07/19/2023
Universality of Spectral Independence with Applications to Fast Mixing in Spin Glasses
We study Glauber dynamics for sampling from discrete distributions μ on ...
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05/23/2023
Set-coloring Ramsey numbers and error-correcting codes near the zero-rate threshold
For positive integers n,r,s with r > s, the set-coloring Ramsey number R...
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05/10/2023
Optimal mixing of the down-up walk on independent sets of a given size
Let G be a graph on n vertices of maximum degree Δ. We show that, for an...
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12/12/2022
Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings
We show that the threshold for the binomial random 3-partite, 3-uniform ...
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10/06/2022
A Toolkit for Robust Thresholds
Consider a host (hyper)graph G which contains a spanning structure due t...
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04/21/2022
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
For appropriate Gaussian processes, Michel Talagrand (1987) proved that ...
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03/31/2022
A Proof of the Kahn-Kalai Conjecture
We prove the "expectation-threshold" conjecture of Kahn and Kalai....
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03/08/2022
Dimension reduction for maximum matchings and the Fastest Mixing Markov Chain
Let G = (V,E) be an undirected graph with maximum degree Δ and vertex co...
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11/05/2021
Entropic Independence II: Optimal Sampling and Concentration via Restricted Modified Log-Sobolev Inequalities
We introduce a framework for obtaining tight mixing times for Markov cha...
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10/29/2021
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training
The mean field (MF) theory of multilayer neural networks centers around ...
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06/08/2021
Entropic Independence in High-Dimensional Expanders: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Polynomials and the Ising Model
We introduce a notion called entropic independence for distributions μ d...
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05/11/2021
Global Convergence of Three-layer Neural Networks in the Mean Field Regime
In the mean field regime, neural networks are appropriately scaled so th...
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05/03/2021
Spectral independence, coupling with the stationary distribution, and the spectral gap of the Glauber dynamics
We present a new lower bound on the spectral gap of the Glauber dynamics...
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02/16/2021
On the sampling Lovász Local Lemma for atomic constraint satisfaction problems
We study the problem of sampling an approximately uniformly random satis...
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11/24/2020
Towards the sampling Lovász Local Lemma
Let Φ = (V, 𝒞) be a constraint satisfaction problem on variables v_1,…, ...
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06/16/2020
A Note on the Global Convergence of Multilayer Neural Networks in the Mean Field Regime
In a recent work, we introduced a rigorous framework to describe the mea...
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01/30/2020