@article{2773, abstract = {Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2].}, author = {László Erdös and Yau, Horng-Tzer}, journal = {Electronic Journal of Probability}, publisher = {Institute of Mathematical Statistics}, title = {{A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices}}, doi = {10.1214/EJP.v17-1779}, volume = {17}, year = {2012}, } @article{2771, abstract = {We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.}, author = {László Erdös and Hasler, David G}, journal = {Journal of Statistical Physics}, number = {5}, pages = {900 -- 923}, publisher = {Springer}, title = {{Anderson localization at band edges for random magnetic fields}}, doi = {10.1007/s10955-012-0445-6}, volume = {146}, year = {2012}, } @article{2778, abstract = {We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification.}, author = {Bourgade, Paul and László Erdös and Yau, Horng-Tzer}, journal = {Journal of Mathematical Physics}, number = {9}, publisher = {American Institute of Physics}, title = {{Bulk universality of general β-ensembles with non-convex potential}}, doi = {10.1063/1.4751478}, volume = {53}, year = {2012}, } @article{2779, abstract = {We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters.}, author = {László Erdös and Hasler, David G}, journal = {Annales Henri Poincare}, number = {8}, pages = {1719 -- 1731}, publisher = {Birkhäuser}, title = {{Wegner estimate for random magnetic Laplacian on ℤ 2}}, doi = {10.1007/s00023-012-0177-9}, volume = {13}, year = {2012}, } @article{2802, abstract = {When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow.}, author = {Lapp, Tobias and Rohloff, Martin and Vollmer, Jürgen T and Björn Hof}, journal = {Experiments in Fluids}, number = {5}, pages = {1187 -- 1200}, publisher = {Springer}, title = {{Particle tracking for polydisperse sedimenting droplets in phase separation}}, doi = {10.1007/s00348-011-1243-7}, volume = {52}, year = {2012}, } @article{2803, abstract = {Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border.}, author = {de Lózar, Alberto and Mellibovsky, Fernando and Avila, Marc and Björn Hof}, journal = {Physical Review Letters}, number = {21}, publisher = {American Physical Society}, title = {{Edge state in pipe flow experiments}}, doi = {10.1103/PhysRevLett.108.214502}, volume = {108}, year = {2012}, } @article{2804, abstract = {The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution}, author = {Blaschke, Johannes and Lapp, Tobias and Björn Hof and Vollmer, Jürgen T}, journal = {Physical Review Letters}, number = {6}, publisher = {American Physical Society}, title = {{Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets}}, doi = {10.1103/PhysRevLett.109.068701}, volume = {109}, year = {2012}, } @inproceedings{2825, abstract = {We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.}, author = {Lampert, Christoph}, location = {Lake Tahoe, NV, United States}, pages = {82 -- 90}, publisher = {Neural Information Processing Systems}, title = {{Dynamic pruning of factor graphs for maximum marginal prediction}}, volume = {1}, year = {2012}, } @article{2848, abstract = {We study evolutionary game theory in a setting where individuals learn from each other. We extend the traditional approach by assuming that a population contains individuals with different learning abilities. In particular, we explore the situation where individuals have different search spaces, when attempting to learn the strategies of others. The search space of an individual specifies the set of strategies learnable by that individual. The search space is genetically given and does not change under social evolutionary dynamics. We introduce a general framework and study a specific example in the context of direct reciprocity. For this example, we obtain the counter intuitive result that cooperation can only evolve for intermediate benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection. Our paper is a step toward making a connection between computational learning theory and evolutionary game dynamics.}, author = {Chatterjee, Krishnendu and Zufferey, Damien and Nowak, Martin}, journal = {Journal of Theoretical Biology}, pages = {161 -- 173}, publisher = {Elsevier}, title = {{Evolutionary game dynamics in populations with different learners}}, doi = {10.1016/j.jtbi.2012.02.021}, volume = {301}, year = {2012}, } @article{2849, author = {Edelsbrunner, Herbert and Strelkova, Nataliya}, journal = {Russian Mathematical Surveys}, number = {6}, pages = {1167 -- 1168}, publisher = {IOP Publishing Ltd.}, title = {{On the configuration space of Steiner minimal trees}}, doi = {10.1070/RM2012v067n06ABEH004820}, volume = {67}, year = {2012}, }