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It is widely accepted that (1) criminalization creates a prudential reason to refrain from the criminalized conduct in order to avoid punishment, and (2) prudence is the wrong reason to refrain from wrongdoing. According to Michael S. Moore, these facts should lead us to conclude that the criminalization of wrongful conduct corrupts motives by making some who would otherwise have refrained from wrongdoing for the right reason, refrain from wrongdoing only out of prudence. This paper argues that (1) and (2) provide no reason to believe that criminalization corrupts motives, but should instead lead us to conclude that the criminalization of wrongful conduct obscures motives by making it harder to identify those who refrain from wrongdoing for the right reason. The paper then goes on to argue that the badness of obscuring motives is a pro tanto reason against criminalizing wrongdoing.

Law and War explores the cultural, historical, spatial, and theoretical dimensions of the relationship between law and war—a connection that has long vexed the jurisprudential imagination. Historically the term \"war crime\" struck some as redundant and others as oxymoronic: redundant because war itself is criminal; oxymoronic because war submits to no law. More recently, the remarkable trend toward the juridification of warfare has emerged, as law has sought to stretch its dominion over every aspect of the waging of armed struggle. No longer simply a tool for judging battlefield conduct, law now seeks to subdue warfare and to enlist it into the service of legal goals. Law has emerged as a force that stands over and above war, endowed with the power to authorize and restrain, to declare and limit, to justify and condemn. In examining this fraught, contested, and evolving relationship, Law and War investigates such questions as: What can efforts to subsume war under the logic of law teach us about the aspirations and limits of law? How have paradigms of law and war changed as a result of the contact with new forms of struggle? How has globalization and continuing practices of occupation reframed the relationship between law and war?

This paper argues that according to the influential version of legal moralism presented by Moore infidelity should all-things-considered be criminalized. This is interesting because criminalizing infidelity is bound to be highly controversial and because Moore’s legal moralism is a prime example of a self-consciously liberal legal moralism, which aims to yield legislative implications that are quite similar to liberalism, while maintaining that morality as such should be legally enforced. Moore tries to make his theory yield such implications, first by claiming that the scope of our moral obligations is much more limited than legal moralists have traditionally claimed, and second by allowing for the possibility that the goodness of legally enforcing morality is often outweighed by the badness of limiting citizens’ morally valuable autonomy and spending scarce resources on enforcement. If Moore is successful in this, legal moralism is strengthened because it becomes immune to many of the most damaging liberal objections. By showing that despite making those moves Moore’s legal moralism is still committed to criminalizing infidelity, a manifestly illiberal implication for legislation, it is established that Moore is unsuccessful in creating a liberal legal moralism, and Moore’s failure in this regard raises questions about whether there can be such a thing as a liberal legal moralism.

In this paper, we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an independent and identically distributed (i.i.d.) fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary measure $\\nu $ . We consider a class of non-square-integrable observables $\\phi $ , mostly of form $\\phi (x)=d(x,x_0)^{-{1}/{\\alpha }}$ , where $x_0$ is a non-recurrent point (in particular a non-periodic point) satisfying some other genericity conditions and, more generally, regularly varying observables with index $\\alpha \\in (0,2)$ . The two types of maps we concatenate are a class of piecewise $C^2$ expanding maps and a class of intermittent maps possessing an indifferent fixed point at the origin. Under conditions on the dynamics and $\\alpha $ , we establish Poisson limit laws, convergence of scaled Birkhoff sums to a stable limit law, and functional stable limit laws in both the annealed and quenched case. The scaling constants for the limit laws for almost every quenched realization are the same as those of the annealed case and determined by $\\nu $ . This is in contrast to the scalings in quenched central limit theorems where the centering constants depend in a critical way upon the realization and are not the same for almost every realization.

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a delta method for nonlinear derivatives. A careful calibration of the norm on the space of probability measures is needed in order to combine differentiability and weak convergence of the underlying empirical process. Based on this, we provide a sufficient and necessary condition for the underlying distribution on the countable metric space for such a distributional limit to hold. We give an explicit form of the limiting distribution for tree spaces. Finally, we apply our findings to optimal transport based inference in large scale problems. An application to nanoscale microscopy is given.

The Sackin index is an important measure for the balance of phylogenetic trees. We investigate two extensions of the Sackin index to the class of galled trees and two of its subclasses, namely simplex galled trees and normal galled trees, where for all classes we consider both labeled and unlabeled galled trees. In all cases, we show that the mean of the Sackin index for a network which is uniformly sampled from its class is asymptotic to for an explicit constant . In addition, we show that the scaled Sackin index converges weakly and with all its moments to the Airy distribution.

We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding random linear program, we characterize under general assumptions the random fluctuations of the empirical optimal solutions around their population quantities after standardization by a distributional limit theorem. Our approach is geometric in nature and further relies on duality and the collection of dual feasible basic solutions. The limiting random variables are driven by the amount of degeneracy inherent in linear programming. In particular, if the corresponding dual linear program is degenerate the asymptotic limit law might not be unique and is determined from the way the empirical optimal solution is chosen. Furthermore, we include consistency and convergence rates of the Hausdorff distance between the empirical and the true optimality sets as well as a limit law for the empirical optimal value involving the set of all dual optimal basic solutions. Our analysis is motivated from statistical optimal transport that is of particular interest here and distributional limit laws for empirical optimal transport plans follow by a simple application of our general theory. The corresponding limit distribution is usually non-Gaussian which stands in strong contrast to recent finding for empirical entropy regularized optimal transport solutions.

Within graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this structure is that of the recursive tree, and we apply its framework within the context of hypergraphs to form hyperrecursive trees, an area that shows promise in network theory. However, when the global profile of these hyperrecursive trees is studied via recursive equations, its recursive nature develops a combinatorial explosion of sorts when deriving mixed moments for higher containment levels. One route to circumvent this issue is through using a special class of urn model, known as an affine urn model, which samples multiple balls at once while maintaining a structure such that the replacement criteria is based on a linear combination of the balls sampled within a draw. We investigate the hyperrecursive tree through its global containment profile, observing the number of vertices found within a particular containment level and, given a set of k containment levels, relate its structure to that of a similar affine urn model in order to derive the asymptotic evolution of its first two mixed moments. We then establish a multivariate central limit theorem for the number of vertices for the first k containment levels. We produce simulations which support our theoretical findings and suggest a relatively quick rate of convergence.

This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. In addition, we use subordination to determine the limit of the largest eigenvalue for the rank-one deformations of unitary-invariant random matrices.