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 manifestationsJournal of Physics A: Mathematical and General.  51. 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 ChainHelvetica Physica Acta.  16:405-435. 2014
2014 Localization for Random Block Operators Related to the XY Spin ChainHelvetica Physica Acta.  16:405-435. 2014
2014 The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gapsMathematical Modelling of Natural Phenomena.  9:44-72. 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 modelsArkiv för Matematik.  51:157-183. 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 dimensionJournal für die reine und angewandte Mathematik.  99-130. 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 applicationsJournal d'Analyse Mathématique.  100:83-116. 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 operatorsHelvetica Physica Acta.  6:309-326. 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 operatorsProceedings of the Indian Academy of Sciences. Mathematical sciences.  112:229-243. 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 operatorsRandom Operators and Stochastic Equations.  6:241-268. 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”Mathematical News / Mathematische Nachrichten.  185:307-307. 1997
1997 Spectral theory for slowly oscillating potentials .2. Schrodinger operators (vol 183, pg 275, 1997)Mathematical News / Mathematische Nachrichten.  185:307-307. 1997
1997 Spectral theory for slowly oscillating potentials II. Schrödinger operatorsMathematical News / Mathematische Nachrichten.  183:275-294. 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 POTENTIALHelvetica Physica Acta.  63:297-314. 1995
1995 One-dimensional Schrödinger operators with local point interactionsJournal für die reine und angewandte Mathematik.  1995:169-186. 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 STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALSReviews in Mathematical Physics.  5:453-456. 1993
1993 APPROXIMATION OF ISOLATED EIGENVALUES OF ORDINARY DIFFERENTIAL-OPERATORSJournal für die reine und angewandte Mathematik.  445:31-44. 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.Journal für die reine und angewandte Mathematik.  1991:1-24. 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.  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

  • 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
  • Full Name

  • Gunter Stolz
  • Blazerid

  • stolz