11 citations · 45 across the 25 of their papers we have counts for
28 papers
Equivalence between Erdős-Hajnal and polynomial Rödl and Nikiforov conjectures
Matija Bucić, Jacob Fox, Huy Tuan Pham
It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős-Hajnal conjec…
A question of Erdős and Graham on Egyptian fractions
David Conlon, Jacob Fox, Xiaoyu He +4
Answering a question of Erdős and Graham, we show that for each fixed positive rational number the number of ways to write as a sum of reciprocals of distinct positive inte…
A multipartite analogue of Dilworth's Theorem
Jacob Fox, Huy Tuan Pham
We prove that every partially ordered set on elements contains subsets such that either each of these subsets has size and, for every…
Homogeneous structures in subset sums and non-averaging sets
David Conlon, Jacob Fox, Huy Tuan Pham
We show that for every positive integer there are positive constants and such that if is a subset of of size at least , then, for so…
Universality of Spectral Independence with Applications to Fast Mixing in Spin Glasses
Nima Anari, Vishesh Jain, Frederic Koehler +2
We study Glauber dynamics for sampling from discrete distributions on the hypercube . Recently, techniques based on spectral independence have successfully yielded…
Optimal mixing of the down-up walk on independent sets of a given size
Vishesh Jain, Marcus Michelen, Huy Tuan Pham +1
Let be a graph on vertices of maximum degree . We show that, for any , the down-up walk on independent sets of size mixes in time $O_{Δ,δ}(k\…
Set-coloring Ramsey numbers and error-correcting codes near the zero-rate threshold
David Conlon, Jacob Fox, Huy Tuan Pham +1
For positive integers with , the set-coloring Ramsey number is the minimum such that if every edge of the complete graph receives a set of c…
Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings
Vishesh Jain, Huy Tuan Pham
We show that the threshold for the binomial random -partite, -uniform hypergraph to contain a Latin square is . We also prove analogous resul…
Small subsets with large sumset: Beyond the Cauchy--Davenport bound
Jacob Fox, Sammy Luo, Huy Tuan Pham +1
For a subset of an abelian group , given its size , its doubling , and a parameter which is small compared to , we study the size of the largest s…
A Toolkit for Robust Thresholds
Huy Tuan Pham, Ashwin Sah, Mehtaab Sawhney +1
Consider a host hypergraph which contains a spanning structure due to minimum degree considerations. We collect three results proving that if the edges of are sampled at th…
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
Jinyoung Park, Huy Tuan Pham
For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than i…
A Proof of the Kahn-Kalai Conjecture
Jinyoung Park, Huy Tuan Pham
Proving the ``expectation-threshold'' conjecture of Kahn and Kalai, we show that for any increasing property on a finite set , $$p_c(\mathcal{F})=O(q(\mathcal{F})\…
Entropic Independence II: Optimal Sampling and Concentration via Restricted Modified Log-Sobolev Inequalities
Nima Anari, Vishesh Jain, Frederic Koehler +2
We introduce a framework for obtaining tight mixing times for Markov chains based on what we call restricted modified log-Sobolev inequalities. Modified log-Sobolev inequalities (M…
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training
Huy Tuan Pham, Phan-Minh Nguyen
The mean field (MF) theory of multilayer neural networks centers around a particular infinite-width scaling, where the learning dynamics is closely tracked by the MF limit. A rando…
Global Convergence of Three-layer Neural Networks in the Mean Field Regime
Huy Tuan Pham, Phan-Minh Nguyen
In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit…
Spectral independence, coupling with the stationary distribution, and the spectral gap of the Glauber dynamics
Vishesh Jain, Huy Tuan Pham, Thuy Duong Vuong
We present a new lower bound on the spectral gap of the Glauber dynamics for the Gibbs distribution of a spectrally independent -spin system on a graph with maximum…
Subset sums, completeness and colorings
David Conlon, Jacob Fox, Huy Tuan Pham
We develop novel techniques which allow us to prove a diverse range of results relating to subset sums and complete sequences of positive integers, including solutions to several l…
Mixing time of fractional random walk on finite fields
Jimmy He, Huy Tuan Pham, Max Wenqiang Xu
We study a random walk on defined by if , and if , where are inde…
On the sampling Lovász Local Lemma for atomic constraint satisfaction problems
Vishesh Jain, Huy Tuan Pham, Thuy-Duong Vuong
We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only…
Regularity method and large deviation principles for the Erdős--Rényi hypergraph
Nicholas A. Cook, Amir Dembo, Huy Tuan Pham
We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our mai…
Towards the sampling Lovász Local Lemma
Vishesh Jain, Huy Tuan Pham, Thuy Duong Vuong
Let be a constraint satisfaction problem on variables such that each constraint depends on at most variables and such that each variable…
A Note on the Global Convergence of Multilayer Neural Networks in the Mean Field Regime
Huy Tuan Pham, Phan-Minh Nguyen
In a recent work, we introduced a rigorous framework to describe the mean field limit of the gradient-based learning dynamics of multilayer neural networks, based on the idea of a…
Tower-type bounds for Roth's theorem with popular differences
Jacob Fox, Huy Tuan Pham, Yufei Zhao
Green developed an arithmetic regularity lemma to prove a strengthening of Roth's theorem on arithmetic progressions in dense sets. It states that for every there is some $N…
Irreducibility of random polynomials of bounded degree
Huy Tuan Pham, Max Wenqiang Xu
It is known that random monic integral polynomials of bounded degree and integral coefficients distributed uniformly and independently in are irreducible over $\mathbb…