Positions

Selected Publications

Academic Article

Year Title Altmetric
2018 Many-body localization in the droplet spectrum of the random XXZ quantum spin chainJournal of Functional Analysis.  275:211-258. 2018
2018 Droplet states in quantum XXZ spin systems on general graphsJournal of Mathematical Physics.  59. 2018
2018 Droplet localization in the random XXZ model and its manifestations 2018
2018 Manifestations of dynamical localization in the disordered XXZ spin chainCommunications in Mathematical Physics.  361:1083-1113. 2018
2017 Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-Periodic Potential in Dimension TwoCommunications in Mathematical Physics.  354:85-113. 2017
2017 Localization properties of the disordered XY spin chain: A review of mathematical results with an eye toward many-body localizationAnnalen der Physik.  529. 2017
2016 Entanglement Dynamics of Disordered Quantum XY ChainsLetters in Mathematical Physics.  106:649-674. 2016
2016 Many-body localization for disordered BosonsNew Journal of Physics.  18. 2016
2016 Localization for transversally periodic random potentials on binary treesJournal of Spectral Theory.  6:557-600. 2016
2015 A uniform area law for the entanglement of eigenstates in the disordered XY chainJournal of Mathematical Physics.  56. 2015
2015 Many-body localization: Concepts and simple modelsMarkov Processes and Related Fields.  21:791-822. 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 systemsJournal of Mathematical Physics.  54. 2013
2013 Simplicity of eigenvalues in Anderson-type models 2013
2012 Quantum Harmonic Oscillator Systems with DisorderJournal of Statistical Physics.  149:969-1012. 2012
2012 Dynamical Localization in Disordered Quantum Spin SystemsCommunications in Mathematical Physics.  315:215-239. 2012
2012 Localization for the random displacement modelDuke Mathematical Journal.  161:587-621. 2012
2011 A continuum version of the Kunz-Souillard approach to localization in one dimension 2011
2011 Spectral properties of the discrete random displacement modelJournal of Spectral Theory.  1:123-153. 2011
2010 A note on fractional moments for the one-dimensional continuum Anderson modelJournal of Mathematical Analysis and Applications.  365:435-446. 2010
2009 Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matricesInternational Mathematics Research Notices.  2009:736-764. 2009
2009 Dynamical localization for unitary anderson modelsMathematical Physics, Analysis and Geometry.  12:381-444. 2009
2009 Low energy properties of the random displacement modelJournal of Functional Analysis.  256:2725-2740. 2009
2009 Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and IndependenceOberwolfach Reports.  2965-2992. 2009
2008 Minimizing the ground state energy of an electron in a randomly deformed latticeCommunications in Mathematical Physics.  283:397-415. 2008
2007 Correlation estimates in the anderson modelJournal of Statistical Physics.  129:649-662. 2007
2007 Lyapunov exponents for unitary Anderson modelsJournal of Mathematical Physics.  48. 2007
2007 Positivity of Lyapunov exponents for anderson-type models on two coupled stringsElectronic Journal of Differential Equations.  2007:1-18. 2007
2007 Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a coneJournal of Mathematical Analysis and Applications.  326:192-208. 2007
2006 Localization near fluctuation boundaries via fractional moments and applications 2006
2006 Lower transport bounds for one-dimensional continuum Schrödinger operatorsMathematische Annalen.  336:361-389. 2006
2006 Moment analysis for localization in random Schrödinger operatorsInventiones Mathematicae.  163:343-413. 2006
2006 Localization for random unitary operatorsLetters in Mathematical Physics.  75:255-272. 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 methodsJournal of Computational and Applied Mathematics.  171:265-276. 2004
2004 Localization for discrete one-dimensional random word modelsJournal of Functional Analysis.  208:423-445. 2004
2003 Delocalization in random polymer modelsCommunications in Mathematical Physics.  233:27-48. 2003
2002 The spectral minimum for random displacement modelsJournal of Computational and Applied Mathematics.  148:133-146. 2002
2002 Localization for one-dimensional, continuum, Bernoulli-Anderson modelsDuke Mathematical Journal.  114:59-100. 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 operatorsTransactions of the American Mathematical Society.  353:635-653. 2001
2000 A generalization of gordon's theorem and applications to quasiperiodic schrödinger operatorsElectronic Journal of Differential Equations.  2000. 2000
2000 Non-monotonic random Schrödinger operators: The Anderson modelJournal of Mathematical Analysis and Applications.  248:173-183. 2000
2000 Localization in one dimensional random media: A scattering theoretic approachCommunications in Mathematical Physics.  213:575-597. 2000
1998 Anderson localization for random schrödinger operators with long range interactionsCommunications in Mathematical Physics.  195:495-507. 1998
1998 Localization for random perturbations of periodic Schrödinger operators 1998
1997 Localization for Schrödinger operators with effective barriersJournal of Functional Analysis.  146:416-429. 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 potentialsProceedings of the American Mathematical Society.  124:2073-2080. 1996
1995 Trace norm estimates for products of integral operators and diffusion semigroupsIntegral Equations and Operator Theory.  23:145-153. 1995
1995 Absence of Absolutely Continuous Spectra for Multidimensional Schrödinger Operators with High BarriersBulletin of the London Mathematical Society.  27:162-168. 1995
1995 Approximation of isolated eigenvalues of general singular ordinary differential operatorsResults in Mathematics.  28:345-358. 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 matricesmanuscripta mathematica.  84:245-260. 1994
1994 Spectral Theory of One-Dimensional Schrödinger Operators with Point InteractionsJournal of Mathematical Analysis and Applications.  184:491-516. 1994
1994 Singular spectrum for multidimensional Schrödinger operators with potential barriersJOURNAL OF OPERATOR THEORY.  32:91-109. 1994
1994 Stability of Spectral Types for Sturm-Liouville OperatorsMathematical Research Letters.  1:437-450. 1994
1993 NOTE TO THE PAPER BY P. D. HISLOP AND S. NAKAMURA: STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS 1993
1993 APPROXIMATION OF ISOLATED EIGENVALUES OF ORDINARY DIFFERENTIAL-OPERATORS 1993
1993 On eigenfunction expansions and scattering theoryMathematische Zeitschrift.  212:337-357. 1993
1992 Polynomial boundedness of eigensolutions and the spectrum of schrödinger operatorsMathematische Annalen.  294:195-211. 1992
1992 Bounded solutions and absolute continuity of Sturm-Liouville operatorsJournal of Mathematical Analysis and Applications.  169:210-228. 1992
1991 On the absolutely continuous spectrum of perturbed periodic Sturm-Liouville operators. 1991
1989 Expansions in generalized eigenfunctions of selfadjoint operatorsMathematische Zeitschrift.  202:397-408. 1989

Book

Year Title Altmetric
2007 Operator Theory, Analysis and Mathematical Physics 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 LOCALIZATION FOR THE RANDOM DISPLACEMENT MODEL 2011
2011 An introduction to the mathematics of Anderson localization.  71-108. 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

  • MA799 - Dissertation Research (Summer Term 2020) 2020
  • MA799 - Dissertation Research (Spring Term 2020) 2020
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2019) 2019
  • MA799 - Dissertation Research (Fall Term 2019) 2019
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2019) 2019
  • MA799 - Dissertation Research (Summer Term 2019) 2019
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2019) 2019
  • MA747 - Linear Ops in Hilbert Space (Spring Term 2019) 2019
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2019) 2019
  • MA799 - Dissertation Research (Spring Term 2019) 2019
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2018) 2018
  • MA698 - M Lev Non-Thesis Res (Summer Term 2018) 2018
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2018) 2018
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2018) 2018
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2018) 2018
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2017) 2017
  • MA485 - Probability (Fall Term 2017) 2017
  • MA585 - Intro to Probability (Fall Term 2017) 2017
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2017) 2017
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2017) 2017
  • MA646 - Real Analysis II (Spring Term 2017) 2017
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2017) 2017
  • MA645 - Real Analysis I (Fall Term 2016) 2016
  • MA698 - M Lev Non-Thesis Res (Summer Term 2016) 2016
  • MA799 - Dissertation Research (Summer Term 2016) 2016
  • MA485 - Probability (Spring Term 2016) 2016
  • MA585 - Intro to Probability (Spring Term 2016) 2016
  • MA646 - Real Analysis II (Spring Term 2016) 2016
  • MA698 - M Lev Non-Thesis Res (Spring Term 2016) 2016
  • MA799 - Dissertation Research (Spring Term 2016) 2016
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2015) 2015
  • MA631 - Linear Algebra (Fall Term 2015) 2015
  • MA698 - M Lev Non-Thesis Res (Fall Term 2015) 2015
  • MA799 - Dissertation Research (Fall Term 2015) 2015
  • MA799 - Dissertation Research (Summer Term 2015) 2015
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2015) 2015
  • MA693 - Special Topics in Mathematics (Spring Term 2015) 2015
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2015) 2015
  • MA799 - Dissertation Research (Spring Term 2015) 2015
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2014) 2014
  • MA648 - Complex Analysis (Fall Term 2014) 2014
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2014) 2014
  • MA799 - Dissertation Research (Fall Term 2014) 2014
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2014) 2014
  • MA799 - Dissertation Research (Summer Term 2014) 2014
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2014) 2014
  • MA646 - Real Analysis II (Spring Term 2014) 2014
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2014) 2014
  • MA799 - Dissertation Research (Spring Term 2014) 2014
  • MA645 - Real Analysis I (Fall Term 2013) 2013
  • MA693 - Special Topics in Mathematics (Fall Term 2013) 2013
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2013) 2013
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2013) 2013
  • EGR265 - Math Tools for Engr Prob Solvi (Spring Term 2013) 2013
  • MA792 - Special Topics in Mathematics (Spring Term 2013) 2013
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2013) 2013
  • MA799 - Dissertation Research (Spring Term 2013) 2013
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2012) 2012
  • MA485 - Probability (Fall Term 2012) 2012
  • MA585 - Intro to Probability (Fall Term 2012) 2012
  • MA698 - M Lev Non-Thesis Res (Fall Term 2012) 2012
  • MA793 - Special Topics in Mathematics (Fall Term 2012) 2012
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2012) 2012
  • MA799 - Dissertation Research (Fall Term 2012) 2012
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2012) 2012
  • MA799 - Dissertation Research (Summer Term 2012) 2012
  • MA692 - Special Topics in Mathematics (Spring Term 2012) 2012
  • MA792 - Special Topics in Mathematics (Spring Term 2012) 2012
  • 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
  • MA793 - Special Topics in Mathematics (Spring Term 2011) 2011
  • MA794 - Special Topics in Mathematics (Spring Term 2011) 2011
  • 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
  • EGR265 - Math Tools for Engr Prob Solvi (Fall Term 2008) 2008
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2008) 2008
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2008) 2008
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2008) 2008
  • MA125 - Calculus I (Fall Term 2007) 2007
  • MA125 - Calculus I (Fall Term 2007) 2007
  • MA693 - Special Topics in Mathematics (Fall Term 2007) 2007
  • MA793 - Special Topics in Mathematics (Fall Term 2007) 2007
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2007) 2007
  • MA799 - Dissertation Research (Fall Term 2007) 2007
  • Education And Training

  • Doctor of Philosophy Level Degree in Mathematics, Goethe University Frankfurt am Main 1989
  • Full Name

  • Gunter Stolz