We prove that every sufficiently large finite planar point set contains either four collinear points or seven points with at most one non-visible pair. More generally, we show that for every fixed graph $H$ with chromatic number at most five, or with chromatic number six and a color-critical edge, the visibility graph...
B. Bhattacharya, Sandip Das, Sk Samim Islam et al.· 0 citations
This paper derives a variational representation for the limiting free energy, whose maximizers determine the asymptotic structure of typical samples from the model, and establishes finite-temperature symmetry breaking for both these models and complement the rigorous results with numerical experiments.
B. Bhattacharya, Pierfrancesco Dionigi, Ankana Ganguly et al.· 0 citations
The joint asymptotic distribution of any finite collection of network moments in random graphs sampled from a graphon, which includes both the nondegenerate case as well as the degenerate case, provides the higher-order fluctuation theory for subgraph counts in the graphon model.
Anirban Chatterjee, S. Dan, B. Bhattacharya· Annals of Statistics· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
