Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane. The leading coefficient $\kappa_n$ is found to satisfy a difference-differential (spatially discrete) equation which is further proved to approach a third order differential equation by double scaling. The third order differential equation is equivalent to the Painlev\'e II equation. The leading coefficient and second leading coefficient of $\phi_n(z)$ can be expressed asymptotically in terms of the Painlev\'e II function.Comment: 16 page

Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 (and with an additional symmetry contraint) they reduce to earlier results for the radial Bullough-Dodd equation.Comment: 29 pages, no figures, LaTeX fil

Reduced O diffusion through Be doped Pt electrodes

Using first principles electronic structure calculations we screen nine elements for their potential to retard oxygen diffusion through poly-crystalline Pt (p-Pt) films. We determine that O diffuses preferentially as interstitial along Pt grain boundaries (GBs). The calculated barriers are compatible with experimental estimates. We find that Be controls O diffusion through p-Pt. Beryllium segregates to Pt GBs at interstitial (i) and substitutional (s) sites. i-Be is slightly less mobile than O and it repels O, thus stuffing the GB. s-Be has a high diffusion barrier and it forms strong bonds to O, trapping O in the GB. Experiments confirm our theoretical predictions.Comment: 3 pages, 2 figure

From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics. Changes in this revision: recomputed Monte Carlo simulations, added reference [19], fit into margins, performed minor editin

Vulnerability, Risk, and the Transition to Adulthood

Examines whether poverty and single parenthood influence the likelihood of risk behavior and dropping out among youth and how these behaviors affect the trajectory of connectedness and employment patterns in adulthood. Considers policy implications

Infants of Depressed Mothers Living in Poverty: Opportunities to Identify and Serve

Examines the prevalence of depression among mothers in poverty by race/ethnicity, age, family structure, prenatal care and feeding practices, and factors such as domestic violence. Explores intervention points and policy initiatives for support services

Negotiated Trade Restrictions with Private Political Pressure

In this paper we consider a home government with political pressure to restrict trade, at the expense of foreigners. The foreign country is compensated with an income transfer, which can be thought of as a portion of the tariff revenues or quota rents. In this setting the two countries should negotiate over the level of tariff and transfer of rents, depending on the level of political pressure at home. However, if this pressure cannot be directly observed abroad, then the home country may have an incentive to claim arbitrarily high political need and seek corresponding high trade barriers . We resolve this problem by determining incentive compatible trade policies, in which the home government has no incentive to overstate (or understate) the political pressure for protection.

The Use of Replacement Workers in Union Contract Negotiations: The U.S. Experience, 1980-1989

It is argued in many circles that a structural change occurred in U.S. collective bargaining in the 1980s. We investigate the extent to which the hiring of replacement workers can account for this change. For a sample of over 300 major strikes since 1980, we estimate the likelihood of replacements being hired. We find that the risk of replacement declines during tight labor markets, and is lower for bargaining units with more experienced workers. We use the predicted replacement risk as an explanatory variable in a model of the union's choice between the strike and holdout threat. We find that strike usage decreases significantly as the predicted replacement risk increases. We estimate that a ban on the use of replacement workers would have increased strike incidence from 1982-1989 by 3 percentage points, a 30 percent increase.

Kids' Share 2008: How Children Fare in the Federal Budget

Provides an annual analysis of trends in federal spending and tax expenditures on children's programs -- such as food stamps, tax credits, and Head Start -- and assesses the impact of future budget planning on children

Two ways to solve ASEP

The purpose of this article is to describe the two approaches to compute exact formulas (which are amenable to asymptotic analysis) for the probability distribution of the current of particles past a given site in the asymmetric simple exclusion process (ASEP) with step initial data. The first approach is via a variant of the coordinate Bethe ansatz and was developed in work of Tracy and Widom in 2008-2009, while the second approach is via a rigorous version of the replica trick and was developed in work of Borodin, Sasamoto and the author in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems