Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams

We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded. Our approach enjoys the simplicity of the Wide Stencil method, but significantly improves its accuracy using ideas from discretizations of optimal transport based on power diagrams. We establish the global convergence of a damped Newton solver for the discrete system of equations. Numerical experiments, in three dimensions, illustrate the scheme efficiency

Do Footprint-based CAFE Standards Make Car Models Bigger?

Corporate Average Fuel Economy (CAFE) standards have historically been set equal across all manufacturer fleets of the same type. Concerns about varying costs across firms and safety implications of standards that are set homogeneously across firms and models resulted in a policy shift towards footprint-based standards. Under this type of standard, individual car models face targets based on the size of the area between the wheelbase and wheel track, so that larger models face less stringent standards, and manufacturers who make, on average, larger cars will face a lighter fleet standard. Theoretical models have shown that this type of policy creates an incentive for firms to effectively lighten the standard they face, but no purely empirical study has tested this theoretical conclusion. I use a series of difference-in-difference estimations to test whether firms respond to the policy by increasing the footprint of individual models. I find some statistically significant evidence of an increase in footprint size in response to the policy when the treatment effect is assumed to increase by market share

Dark matter variations

In this short presentation, we remind of significant unknowns regarding the distribution of Dark Matter in our immediate neighborhood, and review the recent improvements in the obtained limits on its abundance.Comment: 6 pages 1 figure uses \psfrag Corfu Summer Institute Proceeding

Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain

We study the return probability and its imaginary ($\tau$) time continuation after a quench from a domain wall initial state in the XXZ spin chain, focusing mainly on the region with anisotropy $|\Delta|< 1$. We establish exact Fredholm determinant formulas for those, by exploiting a connection to the six vertex model with domain wall boundary conditions. In imaginary time, we find the expected scaling for a partition function of a statistical mechanical model of area proportional to $\tau^2$, which reflects the fact that the model exhibits the limit shape phenomenon. In real time, we observe that in the region $|\Delta|<1$ the decay for large times $t$ is nowhere continuous as a function of anisotropy: it is either gaussian at root of unity or exponential otherwise. As an aside, we also determine that the front moves as $x_{\rm f}(t)=t\sqrt{1-\Delta^2}$, by analytic continuation of known arctic curves in the six vertex model. Exactly at $|\Delta|=1$, we find the return probability decays as $e^{-\zeta(3/2) \sqrt{t/\pi}}t^{1/2}O(1)$. It is argued that this result provides an upper bound on spin transport. In particular, it suggests that transport should be diffusive at the isotropic point for this quench.Comment: 33 pages, 8 figures. v2: typos fixed, references added. v3: minor change