Abel Klein | Academic Influence

Abel Klein's AcademicInfluence.com Rankings

Abel Klein

Mathematics

#1446

World Rank

#2371

Historical Rank

Group Theory

#186

World Rank

#219

Historical Rank

Algebra

#455

World Rank

#617

Historical Rank

Measure Theory

#2846

World Rank

#3386

Historical Rank

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Mathematics

Abel Klein's Degrees

Masters Mathematics Stanford University
Bachelors Mathematics Princeton University

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Why Is Abel Klein Influential?

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According to Wikipedia, Abel Klein is a Brazilian-American mathematician, specializing in mathematical physics and, more specifically, random Schrödinger operators for disordered systems. He received in 1971 his Doctor of Philosophy degree from the Massachusetts Institute of Technology under the supervision of Irving Segal with the thesis Regularity and Covariance Properties of Quantum Fields with Applications to Currents and Generalized Free Fields. Klein was from 1971 to 1972 an adjunct assistant professor at the University of California, Los Angeles, and from 1972 to 1974 an instructor at Princeton University. At the University of California, Irvine's mathematics department, he was from 1974 to 1977 an assistant professor and from 1977 to 1982 an associate professor, and he is from 1982 to the present a full professor; from 1996 to 1999 he was the chair of the department.

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Abel Klein's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A new proof of localization in the Anderson tight binding model (1989) (353)
Anderson localization for Bernoulli and other singular potentials (1987) (296)
Bootstrap Multiscale Analysis and Localization¶in Random Media (2001) (265)
Extended States in the Anderson Model on the Bethe Lattice (1998) (172)
Localization of classical waves I: Acoustic waves (1996) (128)
A characterization of the Anderson metal-insulator transport transition (2004) (111)
Generalized Eigenvalue-Counting Estimates for the Anderson Model (2008) (103)
Localized classical waves created by defects (1997) (99)
A comprehensive proof of localization for continuous Anderson models with singular random potentials (2011) (98)
New Characterizations of the Region of Complete Localization for Random Schrödinger Operators (2005) (92)
Stochastic processes associated with KMS states (1981) (91)
Localization of Classical Waves II: Electromagnetic Waves (1997) (85)
Linear response theory for magnetic Schrödinger operators in disordered media (2004) (83)
Random Schrödinger operators (2008) (79)
Operator kernel estimates for functions of generalized Schrödinger operators (2002) (79)
Midgap Defect Modes in Dielectric and Acoustic Media (1998) (78)
Absolutely Continuous Spectrum in the Anderson Model on the Bethe Lattice (1994) (77)
Multiscale Analysis and Localization of Random Operators (2007) (73)
Simplicity of Eigenvalues in the Anderson Model (2005) (72)
A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model (1986) (70)
Explicit finite volume criteria for localization in continuous random media and applications (2003) (69)
Localization for the Anderson model on a strip with singular potentials (1990) (68)
Dynamical delocalization in random Landau Hamiltonians (2004) (67)
Unique Continuation Principle for Spectral Projections of Schrödinger Operators and Optimal Wegner Estimates for Non-ergodic Random Schrödinger Operators (2012) (64)
Bounds on the density of states for Schrödinger operators (2011) (62)
Construction of a unique self-adjoint generator for a symmetric local semigroup (1981) (62)
Localization for random Schrödinger operators with correlated potentials (1991) (59)
Taming Griffiths' singularities: Infinite differentiability of quenched correlation functions (1995) (59)
On Mott’s formula for the ac-conductivity in the Anderson model (2005) (54)
Localization of light in lossless inhomogeneous dielectrics (1998) (51)
Localization for Schrödinger operators with Poisson random potential (2006) (49)
On Bernoulli decompositions for random variables, concentration bounds, and spectral localization (2007) (48)
From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity (1983) (47)
The Bootstrap Multiscale Analysis for the Multi-particle Anderson Model (2012) (46)
Localization in the ground state of the ising model with a random transverse field (1991) (46)
Spreading of wave packets in the Anderson model on the Bethe Lattice (1996) (44)
EXTINCTION OF CONTACT AND PERCOLATION PROCESSES IN A RANDOM ENVIRONMENT (1994) (44)
Generalized Eigenfunctions for Waves in Inhomogeneous Media (2002) (43)
Localization phenomenon in gaps of the spectrum of random lattice operators (1994) (40)
Smoothness of the density of states in the Anderson model at high disorder (1988) (38)
Periodic Gaussian Osterwalder-Schrader positive processes and the two-sided Markov property on the circle (1981) (38)
Localization of electromagnetic and acoustic waves in random media. Lattice models (1994) (38)
Poisson Statistics for Eigenvalues of Continuum Random Schr (2008) (37)
Supersymmetry and the Parisi-Sourlas dimensional reduction: A rigorous proof (1984) (37)
Sharp inequalities for Weyl operators and Heisenberg groups (1978) (36)
Singular perturbations of positivity preserving semigroups via path space techniques (1975) (35)
Many-body localization in the droplet spectrum of the random XXZ quantum spin chain (2017) (34)
Absolutely continuous spectrum for random Schrödinger operators on the Bethe strip (2011) (34)
Localization in the ground-state of the one dimensionalX−Y model with a random transverse field (1990) (33)
The semigroup characterization of Osterwalder-Schrader path spaces and the construction of Euclidean fields (1978) (33)
Anomalies in the one-dimensional Anderson model at weak disorder (1990) (32)
Smoothness of the density of states in the Anderson model on a one-dimensional strip (1988) (31)
Weak disorder expansion of the invariant measure for the one-dimensional Anderson model (1988) (30)
Analyticity of the density of states in the anderson model on the Bethe lattice (1992) (30)
A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes (2001) (30)
Gaussian OS-positive processes (1977) (29)
On the density of states for random potentials in the presence of a uniform magnetic field (1985) (29)
On localization for the Schrodinger operator with a Poisson random potential (2005) (29)
Decay of two-point functions for (d+1)-dimensional percolation, ising and Potts models withd-dimensional disorder (1991) (28)
A rigorous replica trick approach to Anderson localization in one dimension (1986) (27)
Supersymmetry and dimensional reduction: A non-perturbative proof (1983) (25)
Exponential Moments for Hitting Times of Uniformly Ergodic Markov Processes (1983) (25)
Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models (2013) (25)
Manifestations of Dynamical Localization in the Disordered XXZ Spin Chain (2017) (25)
A General Framework for Localization of Classical Waves: II. Random Media (2004) (24)
The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems (1982) (23)
Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians (2013) (23)
Regularity of the invariant measure and of the density of states in the one-dimensional Anderson model (1990) (21)
An eigensystem approach to Anderson localization (2015) (21)
Ballistic behavior for random Schrödinger operators on the Bethe strip (2011) (21)
Localization at low energies for attractive Poisson random Schr (2006) (20)
Quantization of the Hall Conductance and Delocalization in Ergodic Landau Hamiltonians (2008) (20)
Sub-exponential decay of operator kernels for functions of generalized Schrodinger operators (2004) (20)
On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions (1981) (20)
The conductivity measure for the Anderson model (2007) (19)
Persistence of Anderson localization in Schrödinger operators with decaying random potentials (2006) (19)
Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas (1990) (19)
Localization in the Anderson Model with Long Range Hopping (1993) (19)
Quantitative unique continuation principle for Schr\"odinger Operators with Singular Potentials (2014) (18)
Power-law falloff in two-dimensional Coulomb gases at inverse temperature β>8π (1991) (18)
Regularity of the density of states in the Anderson model on a strip for potentials with singular continuous distributions (1989) (18)
DECOUPLING INEQUALITIES FOR STATIONARY GAUSSIAN PROCESSES (1982) (17)
Localization in the ground state of a disordered array of quantum rotators (1992) (15)
A characterization of Osterwalder-Schrader path spaces by the associated semigroup (1976) (15)
Ising model in a quasiperiodic transverse field, percolation, and contact processes in quasiperiodic environments (1993) (15)
Quadratic expressions in a free boson field (1973) (14)
A Generalization of Markov Processes (1978) (12)
Erratum to “Poisson statistics for eigenvalues of continuum random Schrödinger operators” (2014) (11)
Ac-conductivity and electromagnetic energy absorption for the Anderson model in linear response theory (2014) (10)
Characterization of the Metal–Insulator Transport Transition for the Two-Particle Anderson Model (2016) (7)
The Anderson metal-insulator transport transition (1993) (7)
Eigensystem multiscale analysis for Anderson localization in energy intervals (2016) (7)
Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment (1994) (7)
Eigensystem bootstrap multiscale analysis for the Anderson model (2016) (7)
Renormalized products of the generalized free field and its derivatives. (1973) (7)
Droplet localization in the random XXZ model and its manifestations (2017) (6)
When do Euclidean fields exist? (1976) (6)
Supersymmetry and a two-dimensional reduction in random phenomena (1985) (5)
Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators (2011) (5)
Localization of Light in Randomized Periodic Media (1999) (5)
A Bound on the Averaged Spectral Shift Function and a Lower Bound on the Density of States for Random Schrödinger Operators on ${\mathbb{R}}^{\boldsymbol{d}}$ (2016) (5)
An explicitly solvable model in “Euclidean” field theory: The Fixed Source (1974) (5)
Stochastic processes associated with quantum systems (1981) (4)
Who is Afraid of Griffiths’ Singularities? (1994) (4)
Local behavior of solutions of the stationary Schrödinger equation with singular potentials and bounds on the density of states of Schrödinger operators (2014) (4)
Delocalization for Random Landau Hamiltonians with Unbounded Random Variables (2009) (3)
An upper bound on the energy gap in the (λφ4+σφ2)2 model (1976) (3)
Random Schrödinger Operators: Localization and Delocalization, and All That (2009) (2)
Local Wegner and Minami estimates for continuous random Schr\"odinger operators (2011) (2)
The Liouville equation for singular ergodic magnetic Schr (2008) (2)
The :φ2: Field in theP(φ)2 model (1975) (2)
Random Schr ¨ odinger Operators: Universal Localization, Correlations, and Interactions (2009) (2)
Eigensystem Multiscale Analysis for the Anderson Model via the Wegner Estimate (2019) (2)
Lifshitz tails estimate for the density of states of the Anderson model (Spectra of Random Operators and Related Topics) (2010) (2)
Localization for a continuum Cantor-Anderson Hamiltonian (2007) (1)
The Liouville equation for general ergodic magnetic Schr\"odinger operators (2007) (1)
Quantum Spin Systems in a Random Environment (1992) (1)
Absolutely Continuous Spectrum for Random Schr (2011) (1)
Taming Griffiths' Singularities in Long Range Random Ising Models (1997) (1)
The analytic continuation of a osterwalder-schrader positive representation of the euclidean group to a representation of the poincare group (1984) (1)
Manifestations of Dynamical Localization in the Disordered XXZ Spin Chain (2018) (1)
Localization in the random XXZ quantum spin chain (2022) (1)
Bounds on the density of states for Schrödinger operators (2012) (1)
The Bootstrap Multiscale Analysis for the Multi-particle Anderson Model (2013) (1)
Unique Continuation Principle for Spectral Projections of Schrödinger Operators and Optimal Wegner Estimates for Non-ergodic Random Schrödinger Operators (2013) (1)
Existence of the Kosterlitz-Thouless Phase for Two-Dimensional Coulomb Gases at Inverse Temperatures above 8π (1992) (0)
ABEL KLEIN : publications [ ] (2017) (0)
Bootstrap multiscale analysis and localization (2015) (0)
Eigensystem Multiscale Analysis for the Anderson Model via the Wegner Estimate (2020) (0)
The :φ: Field in the P(φ)2 Model (2004) (0)
Nonlinear Analysis and Optimization II (2010) (0)
Characterization of the Metal–Insulator Transport Transition for the Two-Particle Anderson Model (2017) (0)
Ballistic Behavior for Random Schr (2011) (0)
O ct 2 00 9 THE LIOUVILLE EQUATION FOR SINGULAR ERGODIC MAGNETIC SCHRÖDINGER OPERATORS (2021) (0)
Localization for multi-particle Anderson Hamiltonians & Unique continuation principle for spectral projections (2013) (0)
0 50 30 61 v 2 1 3 Se p 20 05 Simplicity of eigenvalues in the Anderson model (2008) (0)

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