Deterministic reaction models with power-law forces

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished

Global standards of Constitutional law : epistemology and methodology

Just as it led the philosophy of science to gravitate around scientific practice, the abandonment of all foundationalist aspirations has already begun making political philosophy into an attentive observer of the new ways in which constitutional law is practiced. Yet paradoxically, lawyers and legal scholars are not those who understand this the most clearly. Beyond analyzing the jurisprudence that has emerged from the expansion of constitutional justice, and taking into account the development of international and regional law, the ongoing globalization of constitutional law requires comparing the constitutional laws of individual nations. Following Waldron, the product of this new legal science can be considered as ius gentium. This legal science is not as well established as one might like to think. But it can be developed on the grounds of the practice that consists in ascertaining standards. As abstract types of best “practices” (and especially norms) of constitutional law from around the world, these are only a source of law in a substantive, not a formal, sense. They thus belong to what I should like to call a “second order legal positivity.” In this article I will undertake, both at a methodological and an epistemological level, the development of a model for ascertaining global standards of constitutional law

Market Efficiency after the Financial Crisis: It's Still a Matter of Information Costs

Compared to the worldwide financial carnage that followed the Subprime Crisis of 2007-2008, it may seem of small consequence that it is also said to have demonstrated the bankruptcy of an academic financial institution: the Efficient Capital Market Hypothesis (“ECMH”). Two things make this encounter between theory and seemingly inconvenient facts of consequence. First, the ECMH had moved beyond academia, fueling decades of a deregulatory agenda. Second, when economic theory moves from academics to policy, it also enters the realm of politics, and is inevitably refashioned to serve the goals of political argument. This happened starkly with the ECMH. It was subject to its own bubble – as a result of politics, it expanded from a narrow but important academic theory about the informational underpinnings of market prices to a broad ideological preference for market outcomes over even measured regulation. In this Article we examine the Subprime Crisis as a vehicle to return the ECMH to its information cost roots that support a more modest but sensible regulatory policy. In particular, we argue that the ECMH addresses informational efficiency, which is a relative, not an absolute measure. This focus on informational efficiency leads to a more focused understanding of what went wrong in 2007-2008. Yet informational efficiency is related to fundamental efficiency – if all information relevant to determining a security’s fundamental value is publicly available and the mechanisms by which that information comes to be reflected in the securities market price operate without friction, fundamental and informational efficiency coincide. But where all value relevant information is not publicly available and/or the mechanisms of market efficiency operate with frictions, the coincidence is an empirical question both as to the information efficiency of prices and their relation to fundamental value. Properly framing market efficiency focuses our attention on the frictions that drive a wedge between relative efficiency and efficiency under perfect market conditions. So framed, relative efficiency is a diagnostic tool that identifies the information costs and structural barriers that reduce price efficiency which, in turn, provides part of a realistic regulatory strategy. While it will not prevent future crises, improving the mechanisms of market efficiency will make prices more efficient, frictions more transparent, and the influence of politics on public agencies more observable, which may allow us to catch the next problem earlier. Recall that on September 8, 2008, the Congressional Budget Office publicly stated its uncertainty about whether there would be a recession and predicted 1.5 percent growth in 2009. Eight days later, Lehman Brothers had failed, and AIG was being nationalized

Scale-Invariance and the Strong Coupling Problem

The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds - both expanding and contracting - allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in this paper, it is challenging to produce scale-invariant fluctuations that are weakly coupled over the range of wavelengths accessible to cosmological observations. In particular, requiring the background to be a dynamical attractor, the curvature fluctuations are scale-invariant and weakly coupled for at least 10 e-folds only if the background is close to de Sitter space. In this case, the time-translation invariance of the background guarantees time-independent n-point functions. For non-attractor solutions, any predictions depend on assumptions about the evolution of the background even when the perturbations are outside of the horizon. For the simplest such scenario we identify the regions of the parameter space that avoid both classical and quantum mechanical strong coupling problems. Finally, we present extensions of our results to backgrounds in which higher-derivative terms play a significant role.Comment: 17 pages + appendices, 3 figures; v2: typos fixe