Gibbs measures on permutations over one-dimensional discrete point sets

We consider Gibbs distributions on permutations of a locally finite infinite set $X\subset\mathbb{R}$, where a permutation $\sigma$ of $X$ is assigned (formal) energy $\sum_{x\in X}V(\sigma(x)-x)$. This is motivated by Feynman's path representation of the quantum Bose gas; the choice $X:=\mathbb{Z}$ and $V(x):=\alpha x^2$ is of principal interest. Under suitable regularity conditions on the set $X$ and the potential $V$, we establish existence and a full classification of the infinite-volume Gibbs measures for this problem, including a result on the number of infinite cycles of typical permutations. Unlike earlier results, our conclusions are not limited to small densities and/or high temperatures.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1013 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Erhaltung stetiger Symmetrien bei Gibbsschen Punktprozessen in zwei Dimensionen

The conservation of continuous symmetries in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for internal transformations and spatial translations of Gibbsian systems of marked particles with two body-interaction, where the interesting cases of of singular, hard-core and discontinuous interaction are included

Translation-invariance of two-dimensional Gibbsian point processes

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.Comment: 44 pages, 6 figure

THE EFFECT OF REGULATORY MEASURES ON INDIVIDUAL DATA DISCLOSURE: A COUNTRY COMPARISON

Data protection regulations are various. While research has found regulations to be an effective means for privacy in some data disclosure contexts, the ineffectiveness of most cookie banners is a negative example. Therefore, we investigate which contextual factors cause these differing results. Over a series of workshops with legal experts, we identified two main types of regulatory measures: measures with and without user action. Based on dual-process theories, we propose in this research-in-progress that regulations should involve users only in privacy decisions in high-effort contexts and should mandate privacy in low-effort contexts. To investigate this proposition, we plan to conduct a scenario-based survey where participants from six countries disclose data in a high- versus a low-effort context. By applying a hierarchical linear model, we want to group individual differences by regulatory differences of countries. The expected results will show whether effects of different regulatory measures on individual behavior are context-dependent