Publication List

Preprints

• On the spectrum of skew-shift Schrödinger operators [TeX | DVI | PDF].
• Schrödinger operators with potential V(n) = n^-γ cos(2π n^ρ) [TeX | DVI | PDF].
• Localization for random operators with non-monotone potentials with exponentially decaying correlations [TeX | DVI | PDF].
• Discontinuity of the Lyapunov exponent with Z. Gan, [TeX | DVI | PDF].
• On positive Lyapunov exponent for the skew-shift potential. [TeX | DVI | PDF].
• Multiscale Analysis for Ergodic Schrödinger operators and positivity of Lyapunov exponents. [Slides], [TeX | DVI | PDF].
• Unique continuation for discrete nonlinear wave equations, with G. Teschl. [TeX | DVI | PDF].

Publications

• Semiclassical analysis of the largest gap of quasi-periodic Schrödinger operators, Math. Model. Nat. Phenom. (to appear), [TeX | DVI | PDF].
• Optimality of log Hölder continuity of the integrated density of states, with Z. Gan, Math. Nachr. (to appear), [TeX | DVI | PDF].
• Probabilistic averages of Jacobi operators, Comm. Math. Phys. 295:3, 853--875 (2010). [TeX | DVI | PDF].
• A family of Schrödinger Operators whose spectrum is an interval , Comm. Math. Phys. 290:3, 935-939 (2009). [TeX | DVI | PDF].
• Schrödinger Operators defined by Interval Exchange Transformations , with J. Chaika and D. Damanik, J. Mod. Dyn. 3:2, 253-270 (2009), [TeX | DVI | PDF].
• Stability of the Periodic Toda Lattice in the Soliton Region, with G. Teschl, Int. Math. Res. Not. 2009, Art. ID rnp077, 36pp (2009). [TeX | DVI | PDF].
• Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited, with G. Teschl, Rev. Math. Phys. 21:1, 61-109 (2009). [TeX | DVI | PDF].
• Almost Periodic Szegö Cocycles with Uniformly Positive Lyapunov Exponents, with D. Damanik, J. Approx. Theory 161:2, 813-818 (2009). [TeX | DVI | PDF].
• On Perturbations of Quasi-Periodic Schrödinger operators, J. Diff. Eq. (to appear), [TeX | DVI | PDF].
• Long-Time Asymptotics for the Toda Lattice in the Soliton Region, with G.Teschl, Math. Z. 262, 585-602 (2009), [TeX | DVI | PDF].
• Effective Prüfer Angles and Relative Oscillation Criteria, with G. Teschl, J. Diff. Eq. 245, 3823-3848 (2008), [TeX | DVI | PDF].
• Relative Oscillation Theory for Sturm--Liouville operators extended, with G. Teschl, J. Funct. Anal. 254:6, 1702-1720 (2008), [TeX | DVI | PDF].
• Relative Oscillation Theory, weighted Zeros of the Wronskian, and the Spectral Shift Function, with G. Teschl, Comm. Math. Phys. 287:2, 613-640 (2009). [TeX | DVI | PDF].

Informal notes

• The structure of eigenvalues for the skew-shift operator

Thesis

• Positive Lyapunov Exponent for Ergodic Schrödinger Operators, PhD Thesis, Rice University, April 2010. [PDF | PDF (smaller font) | PDF (smaller font,wide) ]
• Relative Oscillation Theory for Sturm-Liouville operators, Master Thesis, University of Vienna, December 2006. [TeX | PDF]