Measure concentration for Euclidean distance in the case of dependent random variables

Let q^n be a continuous density function in n-dimensional Euclidean space. We think of q^n as the density function of some random sequence X^n with values in \BbbR^n. For I\subset[1,n], let X_I denote the collection of coordinates X_i, i\in I, and let \bar X_I denote the collection of coordinates X_i, i\notin I. We denote by Q_I(x_I|\bar x_I) the joint conditional density function of X_I, given \bar X_I. We prove measure concentration for q^n in the case when, for an appropriate class of sets I, (i) the conditional densities Q_I(x_I|\bar x_I), as functions of x_I, uniformly satisfy a logarithmic Sobolev inequality and (ii) these conditional densities also satisfy a contractivity condition related to Dobrushin and Shlosman's strong mixing condition.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000070

Framing the Game: Objections to Bapat’s Game-Theoretic Modeling of the Afghan Surge

In a recently published article in the prestigious journal Foreign Policy Analysis, Navin A. Bapat uses a rationalist approach to explain key bargaining processes related to the Afghanistan conflict, concluding that “the Afghan mission may continue for political reasons until it is impossible to sustain militarily.” The article captures the essence of the strategic situation in Afghanistan: the losing dynamic involved. This brief commentary in response is an attempt to shed light on where the tenets of Bapat’s game-theoretic model may be erroneous, even while the model does produce conclusions that appear valid overall

Growth fluctuations in a class of deposition models

We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where our result turns to current fluctuations of the particles. We use martingale technique and coupling methods to show that, rescaled by time, the variance of the growth as seen by a deterministic moving observer has the form |V-C|*D, where V and C is the speed of the observer and the second class particle, respectively, and D is a constant connected to the equilibrium distribution of the model. Our main result is a generalization of Ferrari and Fontes' result for simple exclusion process. Law of large numbers and central limit theorem are also proven. We need some properties of the motion of the second class particle, which are known for simple exclusion and are partly known for zero range processes, and which are proven here for a type of deposition models and also for a type of zero range processes.Comment: A minor mistake in lemma 5.1 is now correcte

Spindle Starshaped Sets

In this paper, spindle starshaped sets are introduced and investigated, which apart from normalization form an everywhere dense subfamily within the family of starshaped sets. We focus on proving spindle starshaped analogues of recent theorems of Bobylev, Breen, Toranzos, and Zamfirescu on starshaped sets. Finally, we consider the problem of guarding treasures in an art gallery (in the traditional linear way as well as via spindles).Comment: 16 pages, 2 figure

What makes ISAF s/tick: An investigation of the politics of coalition burden-sharing

This paper is interested in conceptualising the often raised issue of over- and under-contributing in coalition operations; that of how and why members of complex coalitions2 may be punching above and below their weight, respectively. To this end, the first section presents a parsimonious baseline assumption regarding what variables may fundamentally inform coalition burden-sharing, to subsequently discuss how much each of these are found to play a role in the Afghanistan context. The second section elaborates on this by assessing the perception and the interpretation of threats by coalition member countries, related to Afghanistan, as this pertains to prioritising other variables within the scheme outlined in the previous section. The third and fourth sections then proceed to examine and further enrich the existing literature on coalition burden-sharing, and provide further insights regarding the operations of the International Security Assistance Force–Afghanistan, and regarding ISAF member-country decisionmaking; the objective here is to generate further refined assumptions, that can permit a preliminary assessment of the phenomenon of uneven burden-sharing in ISAF, complementing the initial baseline expectations