Central limit theorem for crossings in randomly embedded graphs

We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$. Using Stein's method and size-bias coupling, we prove an upper bound on the Kolmogorov distance between the distribution of the number of crossings and a standard normal random variable. As an application, we establish central limit theorems, along with convergence rates, for the number of crossings in random matchings, path graphs, cycle graphs, and the disjoint union of triangles.Comment: 18 pages, 5 figures. This is a merger of arXiv:2104.01134 and arXiv:2205.0399

Racial Politics, Resentment, and Affirmative Action: Asian Americans as “Model” College Applicants

This article uses philosophical analysis to clarify the arguments and claims about racial discrimination brought forward in the recent legal challenges to affirmative action in higher education admissions. Affirmative action opponents argue that elite institutions of higher education are using negative action against Asian American applicants so that they can admit other students of color instead, using race-conscious affirmative action. We examine the surrounding controversy, positing that the portrayal of Asian Americans as a model minority in this debate foments a politics of resentment that divides racial groups. Our analysis centers on how key concepts such as racial discrimination and diversity may be central to this politics of resentment. Given persistent threats to access and equity in higher education, it is important to gain conceptual clarity about the racial politics of anti-affirmative action efforts