@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{2776,
abstract = {We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least 4 + ε moments.},
author = {László Erdös and Knowles, Antti and Yau, Horng-Tzer and Yin, Jun},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {587 -- 640},
publisher = {Springer},
title = {{Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues}},
doi = {10.1007/s00220-012-1527-7},
volume = {314},
year = {2012},
}
@article{243,
abstract = {Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.},
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Geometric and Functional Analysis},
number = {5},
pages = {1124 -- 1190},
publisher = {Springer Basel},
title = {{Quadratic polynomials represented by norm forms}},
doi = {10.1007/s00039-012-0168-5},
volume = {22},
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{2911,
abstract = {We have selected problems that may not yet be well known, but have the
potential to push the research in interesting directions. In particular, we state
problems that do not require specific knowledge outside the standard circle of ideas
in discrete geometry. Despite the relatively simple statements, these problems are
related to current research and their solutions are likely to require new ideas and
approaches. We have chosen problems from different fields to make this short paper
attractive to a wide range of specialists.},
author = {Herbert Edelsbrunner and Ivanov, Alexander and Karasev, Roman},
journal = {Automatic Control and Computer Sciences},
publisher = {Springer},
title = {{Open problems in discrete and computational geometry}},
volume = {in print},
year = {2012},
}