Two-dimensional Gibbsian point processes with continuous spin-symmetries

We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential U. U is supposed to have an internal continuous symmetry. We show that under suitable continuity conditions the considered processes are invariant under the given symmetry. We will achieve this by using Ruelle`s superstability estimates and percolation arguments.Comment: 22 page

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

A role for the cell-wall protein silacidin in cell size of the diatom Thalassiosira pseudonana

Diatoms contribute 20% of global primary production and form the basis of many marine food webs. Although their species diversity correlates with broad diversity in cell size, there is also an intraspecific cell-size plasticity due to sexual reproduction and varying environmental conditions. However, despite the ecological significance of the diatom cell size for food-web structure and global biogeochemical cycles, our knowledge about genes underpinning the size of diatom cells remains elusive. Here, a combination of reverse genetics, experimental evolution and comparative RNA8 sequencing analyses enabled us to identify a previously unknown genetic control of cell size in the diatom Thalassiosira pseudonana. In particular, the targeted deregulation of the expression of the cell-wall protein silacidin caused a significant increase in valve diameter. Remarkably, the natural downregulation of the silacidin gene transcript due to experimental evolution under low temperature also correlated with cell-size increase. Our data give first evidence for a genetically controlled regulation of cell size in Thalassiosira pseudonana and possibly other centric diatoms as they also encode the silacidin gene in their genomes