We construct a new explicit family of good quantum low-density parity-check codes which
additionally have linear time decoders. Our codes are based on a three-term chain (2 m× m) …

Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov
chains are:(i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis …

We prove an optimal mixing time bound for the single-site update Markov chain known as
the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an …

For general spin systems, we prove that a contractive coupling for an arbitrary local Markov
chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a …

We design an FPRAS to count the number of bases of any matroid given by an independent
set oracle, and to estimate the partition function of the random cluster model of any matroid …

For general antiferromagnetic 2-spin systems, including the hardcore model on weighted
independent sets and the antiferromagnetic Ising model, there is an for the partition function …

We introduce a notion called entropic independence that is an entropic analog of spectral
notions of high-dimensional expansion. Informally, entropic independence of a background …

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis
Gharan) from the Boolean domain to general discrete domains. This property characterises …

The spectral independence approach of Anari et al.(2020) utilized recent results on high-
dimensional expanders of Alev and Lau (2020) and established rapid mixing of the Glauber …

We show fully polynomial time randomized approximation schemes (FPRAS) for counting
matchings of a given size, or more generally sampling/counting monomer-dimer systems in …