Vishesh Jain | DeepAI

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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 ...

0 Nima Anari, et al. ∙

∙ 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...

0 Vishesh Jain, et al. ∙

∙ 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 ...

0 Vishesh Jain, et al. ∙

∙ 06/09/2022

Spencer's theorem in nearly input-sparsity time

A celebrated theorem of Spencer states that for every set system S_1,…, ...

0 Vishesh Jain, et al. ∙

∙ 05/03/2022

Optimal minimization of the covariance loss

Let X be a random vector valued in ℝ^m such that X_2≤ 1 almost surely. F...

0 Vishesh Jain, et al. ∙

∙ 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...

0 Vishesh Jain, et al. ∙

∙ 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...

0 Nima Anari, et al. ∙

∙ 08/02/2021

Approximate counting and sampling via local central limit theorems

We give an FPTAS for computing the number of matchings of size k in a gr...

0 Vishesh Jain, et al. ∙

∙ 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...

0 Nima Anari, et al. ∙

∙ 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...

0 Vishesh Jain, et al. ∙

∙ 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...

0 Vishesh Jain, et al. ∙

∙ 01/19/2021

Anticoncentration versus the number of subset sums

Let w⃗ = (w_1,…, w_n) ∈ℝ^n. We show that for any n^-2≤ϵ≤ 1, if #{ξ⃗...

0 Vishesh Jain, et al. ∙

∙ 11/24/2020

Towards the sampling Lovász Local Lemma

Let Φ = (V, 𝒞) be a constraint satisfaction problem on variables v_1,…, ...

0 Vishesh Jain, et al. ∙

∙ 09/03/2020

On the smoothed analysis of the smallest singular value with discrete noise

Let A be an n× n real matrix, and let M be an n× n random matrix whose e...

0 Vishesh Jain, et al. ∙

∙ 07/13/2020

Perfectly Sampling k≥ (8/3 +o(1))Δ-Colorings in Graphs

We present a randomized algorithm which takes as input an undirected gra...

0 Vishesh Jain, et al. ∙

∙ 05/18/2020

On the real Davies' conjecture

We show that every matrix A ∈R^n× n is at least δ A-close to a real ...

0 Vishesh Jain, et al. ∙

∙ 03/23/2020

Kac meets Johnson and Lindenstrauss: a memory-optimal, fast Johnson-Lindenstrauss transform

Based on the Kac random walk on the orthogonal group, we present a fast ...

0 Vishesh Jain, et al. ∙

∙ 08/29/2019

Smoothed analysis of the least singular value without inverse Littlewood-Offord theory

We study the lower tail behavior of the least singular value of an n× n ...

0 Vishesh Jain, et al. ∙

∙ 05/24/2019

Accuracy-Memory Tradeoffs and Phase Transitions in Belief Propagation

The analysis of Belief Propagation and other algorithms for the reconst...

0 Vishesh Jain, et al. ∙

∙ 09/13/2018

Towards the linear arboricity conjecture

The linear arboricity of a graph G, denoted by la(G), is the minimum num...

0 Asaf Ferber, et al. ∙

∙ 08/22/2018

Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective

The free energy is a key quantity of interest in Ising models, but unfor...

0 Vishesh Jain, et al. ∙

∙ 03/28/2018

1-factorizations of pseudorandom graphs

A 1-factorization of a graph G is a collection of edge-disjoint perfect ...

0 Asaf Ferber, et al. ∙

∙ 02/16/2018

The Vertex Sample Complexity of Free Energy is Polynomial

We study the following question: given a massive Markov random field on ...

0 Vishesh Jain, et al. ∙

∙ 02/16/2018

The Mean-Field Approximation: Information Inequalities, Algorithms, and Complexity

The mean field approximation to the Ising model is a canonical variation...

0 Vishesh Jain, et al. ∙

∙ 11/05/2017

Approximating Partition Functions in Constant Time

We study approximations of the partition function of dense graphical mod...

0 Vishesh Jain, et al. ∙

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