Phase transitions of extremal cuts for the configuration model

The $k$-section width and the Max-Cut for the configuration model are shown to exhibit phase transitions according to the values of certain parameters of the asymptotic degree distribution. These transitions mirror those observed on Erd\H{o}s-R\'enyi random graphs, established by Luczak and McDiarmid (2001), and Coppersmith et al. (2004), respectively

Universality for critical heavy-tailed network models: Metric structure of maximal components

We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such results were derived by Bhamidi, van der Hofstad, Sen [Probab. Theory Relat. Fields 2018]. We develop general principles under which the identical scaling limits as the rank-one case can be obtained. Of independent interest, we derive refined asymptotics for various susceptibility functions and the maximal diameter in the barely subcritical regime.Comment: Final published version. 47 pages, 6 figure

Global lower mass-bound for critical configuration models in the heavy-tailed regime

We establish the global lower mass-bound property for the largest connected components in the critical window for the configuration model when the degree distribution has an infinite third moment. The scaling limit of the critical percolation clusters, viewed as measured metric spaces, was established in [7] with respect to the Gromov-weak topology. Our result extends those scaling limit results to the stronger Gromov-Hausdorff-Prokhorov topology under slightly stronger assumptions on the degree distribution. This implies the distributional convergence of global functionals such as the diameter of the largest critical components. Further, our result gives a sufficient condition for compactness of the random metric spaces that arise as scaling limits of critical clusters in the heavy-tailed regime.Comment: 25 page

Etiology and risk factors of ischemic stroke in Indian-American patients from a hospital-based registry in New Jersey, USA

Background and Objective: The stroke center at the New Jersey Neuroscience Institute is located in Edison township in New Jersey which has one of the largest fractions of Asian immigrants in USA. This study aims to compare risk factors and etiology of ischemic stroke in patients of Indian origin with those of the White-Americans. Methods: Information pertaining to stroke risk factors was prospectively collected between July 2005 to June 2008. The patients underwent a stroke work-up, which included computerized tomograms, magnetic resonance imaging and magnetic resonance angiography of brain, carotid duplex, Holter monitoring and two dimensional echocardiogram. Etiology of ischemic stroke was ascertained using the classification developed for the Trial of Org 10172 in Acute Stroke Treatment (TOAST). Results: The data of 378 patients (mean age = 71±12 years, 54% females, White-Americans=347) with ischemic stroke were collected over 3 years. The 31 Indian patients (mean age = 64±10 years) had a higher proportion of diabetics mellitus (p=0.001) and were signifi cantly younger than the White-Americans. There were signifi cantly lower proportion of persons who smoked (p=0.03) or used alcohol (p=0.03). The commonest cause of ischemic stroke was small vessel occlusive disease, rather than large artery atherosclerosis among the White-Americans (p=0.009). Conclusions: when compared to White-Americans, The Indian-American developed stroke at a younger age, despite a lower rate of alcohol and tobacco use. They have a higher prevalence of diabetes and physical inactivity. The commonest cause of ischemic stroke was small vessel occlusive disease