Hierarchical pinning model with site disorder: Disorder is marginally relevant

We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case [6, 9], there exists a value of a parameter b (enters in the definition of the hierarchical lattice) that separates an irrelevant disorder regime and a relevant disorder regime. We show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model. The proof goes beyond the technique used in [9] and it takes explicitly advantage of the inhomogeneous character of the Green function of the model.Comment: 13 pages, 1 figure, final version accepted for publication. to appear in Probability Theory and Related Field

The Simple Exclusion Process on the Circle has a diffusive Cutoff Window

In this paper, we investigate the mixing time of the simple exclusion process on the circle with $N$ sites, with a number of particle $k(N)$ tending to infinity, both from the worst initial condition and from a typical initial condition. We show that the worst-case mixing time is asymptotically equivalent to $(8\pi^2)^{-1}N^2\log k$, while the cutoff window, is identified to be $N^2$. Starting from a typical condition, we show that there is no cutoff and that the mixing time is of order $N^2$.Comment: 37 pages, 3 Figure

Employment-Based Health Insurance: 2010

[Excerpt] This report uses data from the Survey of Income and Program Participation (SIPP) to examine the characteristics of people with employer-provided health insurance coverage as well as characteristics of employers that offer health insurance. This documentation of the current distribution of employment-based health insurance coverage across socioeconomic characteristics is needed to establish the changes associated with recent health care legislation. The report is composed of two sections. The first section provides a brief overview of historical trends in employer-provided coverage rates by source of coverage as well as the reasons for nonparticipation in health insurance from 1997 to 2010. The second section focuses on data collected in 2010 and describes health insurance offer and take-up rates by employee and employer characteristics. In addition, the report describes the insurance status of workers not participating in an employer’s plan and the reasons for nonparticipation