Asymptotic Results for Configuration Model Random Graphs with Arbitrary Degree Distributions (2010)

09/27/2010 at 10:38 pm

Luke Fostvedt, Dan Nordman, Alyson Wilson

Abstract: We consider a model for generating a random graph using the configuration model. In the configuration model, each node draws a degree independently from a marginal degreed distribution and endpoints pair randomly. We establish non-trivial bounds on the expected sizes of “buckets ” for large graphs. We define nodes i and j in a graph as neighbors if they share an edge, and we define the “bucket ” associated with node i as the set of nodes that are its neighbors and have degree greater than node i. We formalize this argument by providing an analysis for the expected number of items and pairs in a “bucket ” for arbitrarily specified degree distributions, which include power laws.

Paper: Technical Report

Fixed-cost vs. Fixed-risk post-election audits in Iowa

09/12/2010 at 10:31 pm

Jonathan Hobbs, Luke Fostvedt, Adam Pintar, David Rockoff, Eunice Kim, and Randy Griffiths

Electoral integrity has been a forefront issue during the past decade. Policy developments such as voter-verified paper records and post-election audits bolster transparency and voter confidence.

paper: pdf

Measure Theory and Probability Theory Study Guide

12/29/2009 at 9:24 am

Study Guide compiled by Cory Lanker and Luke Fostvedt, Iowa State University
Content includes: Sigma Algebras, Measurable Sets, Lebesgue Measures, Lebesgue Integration, General Lebesgue Integrals, Product Measures, Radon-Nikodym Theorem, Fubini and Tonelli’s theorems, Lebesgue Fundamental Theorem of Calculus, Inequalities, Independence, Borel-Cantelli Lemmas, Law of Large Numbers, Convergence in Probability, Convergence is Distribution, Kolmogorov Theorems, Continuous Mapping Theorem, Tightness, and Method of Moments.

Source: class notes by Dan Nordman, Fall 2009, STAT642, and “Real Analysis” by H. Royden and “Measure Theory” by P.R. Halmos. All references in this document are to Professor Dan Nordman’s class notes.
Content: This study guide is a good supplement to the Athreya Lahiri Text.

Study Guide: Measure Theory and Probability Theory Study Guide