We revisit a classic topic in probabilistic combinatorics, the lower-tail large-deviation problem for triangles in the random graph $G(n,p)$. Here we aim for first-order asymptotics for the quantity $\mathbb{P}[X=k]$ with $X$ the number of triangles in $G(n,p)$ and $0 \le k \le (1-\epsilon) \mathbb{E}X$, in the sparse...
Jade Lintott, Will Perkins, Corrine Yap· 0 citations
We study deterministic approximation algorithms for the permanent of a nonnegative matrix through the Bethe permanent, an approximation computable in polynomial time. The tight analysis of Anari and Rezaei gives a universal comparison between the permanent and the Bethe permanent within a factor $(\sqrt 2)^n$. The simp...
The worst-case tractability of approximate counting and sampling of fixed-size slices for bipartite independent set problems for bipartite independent set problems is studied.
Ijay Narang, Will Perkins, Yu-Zhou Wang et al.· 1 citation
The main idea is to introduce a family of quadratic tilts in the left-right occupation imbalance and show that each tilted measure can be sampled efficiently using Glauber dynamics, and obtain efficient approximate counting and sampling at every fugacity $\lambda>0$ whenever.
Ijay Narang, Will Perkins· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
