@inproceedings{2105, author = {Skouras, Mélina and Thomaszewski, Bernhard and Bernd Bickel and Groß, Markus S}, number = {2}, pages = {835 -- 844}, publisher = {Wiley-Blackwell}, title = {{Computational design of rubber balloons}}, doi = {10.1111/j.1467-8659.2012.03064.x}, volume = {31}, year = {2012}, } @article{2125, abstract = {We consider a class of stochastic PDEs of Burgers type in spatial dimension 1, driven by space–time white noise. Even though it is well known that these equations are well posed, it turns out that if one performs a spatial discretization of the nonlinearity in the “wrong” way, then the sequence of approximate equations does converge to a limit, but this limit exhibits an additional correction term. This correction term is proportional to the local quadratic cross-variation (in space) of the gradient of the conserved quantity with the solution itself. This can be understood as a consequence of the fact that for any fixed time, the law of the solution is locally equivalent to Wiener measure, where space plays the role of time. In this sense, the correction term is similar to the usual Itô–Stratonovich correction term that arises when one considers different temporal discretizations of stochastic ODEs.}, author = {Hairer, Martin M and Jan Maas}, journal = {Annals of Probability}, number = {4}, pages = {1675 -- 1714}, publisher = {Institute of Mathematical Statistics}, title = {{A spatial version of the Itô-Stratonovich correction}}, doi = {10.1214/11-AOP662}, volume = {40}, year = {2012}, } @article{2127, abstract = {We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry–Émery and Otto–Villani. Further, we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.}, author = {Erbar, Matthias and Jan Maas}, journal = {Archive for Rational Mechanics and Analysis}, number = {3}, pages = {997 -- 1038}, publisher = {Springer}, title = {{Ricci curvature of finite Markov chains via convexity of the entropy}}, doi = {10.1007/s00205-012-0554-z}, volume = {206}, year = {2012}, } @article{2128, abstract = {We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces T 1,q of Coifman–Meyer–Stein.}, author = {Jan Maas and van Neerven, Jan M and Portal, Pierre}, journal = {Arkiv för Matematik}, number = {2}, pages = {379 -- 395}, publisher = {Springer}, title = {{Whitney coverings and the tent spaces T 1,q (γ) for the Gaussian measure}}, doi = {10.1007/s11512-010-0143-z}, volume = {50}, year = {2012}, } @article{2203, abstract = {We show that the electric dipole-dipole interaction between a pair of polar molecules undergoes an all-out transformation when superimposed by a far-off-resonant optical field. The combined interaction potential becomes tunable by variation of wavelength, polarisation and intensity of the optical field and its dependence on the intermolecular separation exhibits a crossover from an inverse-power to an oscillating behaviour. The ability thereby offered to control molecular interactions opens up avenues toward the creation and manipulation of novel phases of ultracold polar gases among whose characteristics is a long-range entanglement of the dipoles' mutual orientation. We devised an accurate analytic model of such optical-field-dressed dipole-dipole interaction potentials, which enables a straightforward access to the optical-field parameters required for the design of intermolecular interactions in the laboratory.}, author = {Mikhail Lemeshko and Friedrich, Břetislav}, journal = {Molecular Physics}, number = {15-16}, pages = {1873 -- 1881}, publisher = {Taylor & Francis}, title = {{Interaction between polar molecules subject to a far-off-resonant optical field: Entangled dipoles up- or down-holding each other}}, doi = {10.1080/00268976.2012.689868}, volume = {110}, year = {2012}, }