Positions

Selected Publications

Academic Article

Year Title Altmetric
2018 Many-body localization in the droplet spectrum of the random XXZ quantum spin chain 2018
2018 Droplet states in quantum XXZ spin systems on general graphs 2018
2018 Droplet localization in the random XXZ model and its manifestations 2018
2018 Manifestations of dynamical localization in the disordered XXZ spin chain 2018
2017 Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-Periodic Potential in Dimension Two 2017
2017 Localization properties of the disordered XY spin chain: A review of mathematical results with an eye toward many-body localization 2017
2016 Entanglement Dynamics of Disordered Quantum XY Chains 2016
2016 Many-body localization for disordered Bosons 2016
2016 Localization for transversally periodic random potentials on binary trees 2016
2015 A uniform area law for the entanglement of eigenstates in the disordered XY chain 2015
2015 Many-body localization: Concepts and simple models 2015
2014 Localization for Random Block Operators Related to the XY Spin Chain 2014
2014 Localization for Random Block Operators Related to the XY Spin Chain 2014
2014 The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gaps 2014
2013 An area law for the bipartite entanglement of disordered oscillator systems 2013
2013 Simplicity of eigenvalues in Anderson-type models 2013
2012 Quantum Harmonic Oscillator Systems with Disorder 2012
2012 Dynamical Localization in Disordered Quantum Spin Systems 2012
2012 Localization for the random displacement model 2012
2011 A continuum version of the Kunz-Souillard approach to localization in one dimension 2011
2011 Spectral properties of the discrete random displacement model 2011
2010 A note on fractional moments for the one-dimensional continuum Anderson model 2010
2009 Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices 2009
2009 Dynamical localization for unitary anderson models 2009
2009 Low energy properties of the random displacement model 2009
2009 Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence 2009
2008 Minimizing the ground state energy of an electron in a randomly deformed lattice 2008
2007 Correlation estimates in the anderson model 2007
2007 Lyapunov exponents for unitary Anderson models 2007
2007 Positivity of Lyapunov exponents for anderson-type models on two coupled strings 2007
2007 Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone 2007
2006 Localization near fluctuation boundaries via fractional moments and applications 2006
2006 Lower transport bounds for one-dimensional continuum Schrödinger operators 2006
2006 Moment analysis for localization in random Schrödinger operators 2006
2006 Localization for random unitary operators 2006
2005 Absence of continuous spectral types for certain non-stationary random schrödinger operators 2005
2004 Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: Elementary methods 2004
2004 Localization for discrete one-dimensional random word models 2004
2003 Delocalization in random polymer models 2003
2002 The spectral minimum for random displacement models 2002
2002 Localization for one-dimensional, continuum, Bernoulli-Anderson models 2002
2002 Strategies in localization proofs for one-dimensional random Schrödinger operators 2002
2001 Two-parameter spectral averaging and localization for non-monotonic random schrödinger operators 2001
2000 A generalization of gordon's theorem and applications to quasiperiodic schrödinger operators 2000
2000 Non-monotonic random Schrödinger operators: The Anderson model 2000
2000 Localization in one dimensional random media: A scattering theoretic approach 2000
1998 Anderson localization for random schrödinger operators with long range interactions 1998
1998 Localization for random perturbations of periodic Schrödinger operators 1998
1997 Localization for Schrödinger operators with effective barriers 1997
1997 Errata in the paper: “Spectral theory for slowly oscillating potentials. II. Schrödinger operators” 1997
1997 Spectral theory for slowly oscillating potentials .2. Schrodinger operators (vol 183, pg 275, 1997) 1997
1997 Spectral theory for slowly oscillating potentials II. Schrödinger operators 1997
1996 Operators with singular continuous spectrum, V. Sparse potentials 1996
1995 Trace norm estimates for products of integral operators and diffusion semigroups 1995
1995 Absence of Absolutely Continuous Spectra for Multidimensional Schrödinger Operators with High Barriers 1995
1995 Approximation of isolated eigenvalues of general singular ordinary differential operators 1995
1995 LOCALIZATION FOR RANDOM SCHRODINGER-OPERATORS WITH POISSON POTENTIAL 1995
1995 One-dimensional Schrödinger operators with local point interactions 1995
1994 Spectral theory for slowly oscillating potentials I. Jacobi matrices 1994
1994 Spectral Theory of One-Dimensional Schrödinger Operators with Point Interactions 1994
1994 Singular spectrum for multidimensional Schrödinger operators with potential barriers 1994
1994 Stability of Spectral Types for Sturm-Liouville Operators 1994
1993 STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS 1993
1993 APPROXIMATION OF ISOLATED EIGENVALUES OF ORDINARY DIFFERENTIAL-OPERATORS 1993
1993 On eigenfunction expansions and scattering theory 1993
1992 Polynomial boundedness of eigensolutions and the spectrum of schrödinger operators 1992
1992 Bounded solutions and absolute continuity of Sturm-Liouville operators 1992
1991 On the absolutely continuous spectrum of perturbed periodic Sturm-Liouville operators. 1991
1989 Expansions in generalized eigenfunctions of selfadjoint operators 1989

Book

Year Title Altmetric
2007 Operator theory, analysis and mathematical physics.  Ed. 174.  2007

Chapter

Year Title Altmetric
2012 Understanding the random displacement model: From ground state properties to localization.  183-219. 2012
2012 Understanding the random displacement model: from ground state properties to localization.  183-219. 2012
2011 An introduction to the mathematics of Anderson localization.  71-108. 2011
2011 Localization for the random displacement model.  169-175. 2011
2006 Fractional moment methods for Anderson localization in the continuum.  619-625. 2006
2002 Lyapunov exponents in continuum Bernoulli-Anderson models.  121-130. 2002
1999 Monotonicity versus non-monotonicity in random operators.  365-371. 1999
1997 Band edge localization in randomly perturbed crystals.  184-191. 1997
1997 Sturm-Liouville problems with an infinite number of interior singularities.  211-249. 1997
1995 Localization for the Poisson model.  375-380. 1995
1994 Results in the spectral theory of Schrödinger operators with wide potential barriers.  27-32. 1994
1990 Expansions in generalized eigenfunctions of Schrödinger operators with singular potentials.  353-372. 1990

Teaching Activities

  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2019) 2019
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  • MA698 - M Lev Non-Thesis Res (Summer Term 2018) 2018
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2018) 2018
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  • MA645 - Real Analysis I (Fall Term 2016) 2016
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  • MA485 - Probability (Spring Term 2016) 2016
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  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2012) 2012
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  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2012) 2012
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2011) 2011
  • MA698 - M Lev Non-Thesis Res (Summer Term 2011) 2011
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2011) 2011
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2011) 2011
  • MA693 - Special Topics in Mathematics (Spring Term 2011) 2011
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  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2011) 2011
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2010) 2010
  • MA631 - Algebra II (Fall Term 2010) 2010
  • MA693 - Special Topics in Mathematics (Fall Term 2010) 2010
  • MA793 - Special Topics in Mathematics (Fall Term 2010) 2010
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2010) 2010
  • MA698 - M Lev Non-Thesis Res (Summer Term 2010) 2010
  • MA799 - Dissertation Research (Summer Term 2010) 2010
  • MA646 - Real Analysis II (Spring Term 2010) 2010
  • MA691 - Mathematics Seminar (Spring Term 2010) 2010
  • MA799 - Dissertation Research (Spring Term 2010) 2010
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2009) 2009
  • MA645 - Real Analysis I (Fall Term 2009) 2009
  • MA799 - Dissertation Research (Fall Term 2009) 2009
  • MA799 - Dissertation Research (Summer Term 2009) 2009
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2009) 2009
  • MA799 - Dissertation Research (Spring Term 2009) 2009
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  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2008) 2008
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  • MA125 - Calculus I (Fall Term 2007) 2007
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  • Full Name

  • Gunter Stolz