Determinantal probability measures

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation, involving Hilbert spaces, combinatorics, homology, and group representations, among other areas.Comment: 50 pp; added reference to revision. Revised introduction and made other small change

Will the New U.K. Competition and Markets Authority Make Better Antitrust Decisions?

The United Kingdom has a unique set of institutions charged with enforcing competition law. The twin pillars are the Competition Commission (“CC”) and the Office of Fair Trading (“OFT”). In the coming parliament, legislation will be passed to merge them into a new Competition and Markets Authority (“CMA”), probably with effect from 2014.2 They each have a high reputation and are regularly ranked alongside the DOJ, FTC, and DG Competition as among the best in the world. OK, few would argue that any of these institutions is unimprovable, but it does mean there is much that could be lost if the CMA is less effective than its predecessors. Should we be worried

Factors of IID on Trees

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well. Despite recent spectacular progress of Bowen, the situation for non-amenable groups, including free groups, is still largely mysterious. We present some illustrative results and open questions on free groups, which are particularly interesting in combinatorics, statistical physics, and probability. Our results include bounds on minimum and maximum bisection for random cubic graphs that improve on all past bounds.Comment: 18 pages, 1 figur

Palestinian terrorist organizations

This paper acts as a source of information on Hamas and its relationships with the other terrorist groups. It also provides evidence for the prominent role of Hamas in the future of the Arab-Israeli conflict