Rapid mixing of Swendsen-Wang dynamics in two dimensions

We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the random-cluster model on arbitrary graphs. In particular, we prove that rapid mixing of HB implies rapid mixing of SW on graphs with bounded maximum degree and that rapid mixing of SW and rapid mixing of SB are equivalent. Additionally, the spectral gap of SW and SB on planar graphs is bounded from above and from below by the spectral gap of these dynamics on the corresponding dual graph with suitably changed temperature. As a consequence we obtain rapid mixing of the Swendsen-Wang dynamics for the Potts model on the two-dimensional square lattice at all non-critical temperatures as well as rapid mixing for the two-dimensional Ising model at all temperatures. Furthermore, we obtain new results for general graphs at high or low enough temperatures.Comment: Ph.D. thesis, 66 page

“Normal citizens” versus “Rowdies”: police categorisations of protesters in Germany

The paper investigates police perceptions of protesters. Based on group discussions with riot police and interviews with high ranking officers, six domains are analysed as dimensions of a risk constellation contributing to the emergence of an enemy image of the protester. The findings suggest that labels describing the “police counterpart” often express distance and opposition (1) and depoliticise demonstrations (2). Furthermore, formal (3) and informal (4) categorisations of protesters as well as the perception of indications of threat in policing practice (5) are examined. Bipolar patterns of classification of protesters were found to be influential. Classifications are partly based in the law and partly in particularistic and normative subcultural attributions of legitimacy which police transfer into their organisational interpretive schemata distinguishing between legality/illegality. For explanatory means the study utilises perspectives of organisational sociology as well as the cultural distance between the police and the protesters (6). This is further elaborated using the social figure of the “normal citizen”, in which specific police conceptions of normality are condensed and which serves as a threshold for the perception of deviant protesters. Besides the implications for theory of democracy of the analysed clichés and enemy images the findings conclusively suggest that the distanced to hostile relationship between the police and some protesters does not merely represent a pedagogical or “practical” problem of the police, but is the expression of a certain conflict structure. In this structure organisational and individual factors on the side of the police as well as their actual conflict experience at demonstrations converge

Rapid mixing of Swendsen-Wang and single-bond dynamics in two dimensions

We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model on arbitrary graphs with m edges is bounded above by 16 m log m times the spectral gap of the single-bond (or heat-bath) dynamics. This and the corresponding lower bound imply that rapid mixing of these two dynamics is equivalent. Using the known lower bound on the spectral gap of the Swendsen-Wang dynamics for the two dimensional square lattice $Z_L^2$ of side length L at high temperatures and a result for the single-bond dynamics on dual graphs, we obtain rapid mixing of both dynamics on $\Z_L^2$ at all non-critical temperatures. In particular this implies, as far as we know, the first proof of rapid mixing of a classical Markov chain for the Ising model on $\Z_L^2$ at all temperatures.Comment: 20 page

Market discipline and the use of government bonds as collateral in the EMU

The confidence that financial markets are able to discipline the debt behaviour of governments is not very high. Therefore, the Stability and Growth Pact has been implemented as an institutional constraint to substitute for the market mechanism. With the weakening of the Pact, market discipline could gain importance again. To strengthen market discipline, reasons for its failure in the euro area have to be analysed. One possible reason could be that the European Central Bank accepts all European government bonds without distinction in its monetary policy auctions as collateral. This could provide the financial market with a signal that these government securities are equally (non-)risky and that a differentiation with respect to risk premia is not needed. --Stability and Growth Pact,Market Discipline,Collateral,Repo

Haar projection numbers and failure of unconditional convergence in Sobolev spaces

For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of projection operators depending on properties of the Haar frequency set