Publication list:
Preprints:
To appear:
Published:
- WKB
asymptotics of meromorphic solutions to difference
equations.
In collaboration with A. Fedotov.
Appl. Anal. 100 (2021), no. 7, 1557--1573.
- Interacting
electrons in a random medium: a simple one-dimensional
model
In collaboration with N. Veniaminov.
In
"Frontiers in Analysis and Probability", pp. 91--242, Springer
Verlag (2020)
Eds : Anantharaman, N., Nikeghbali, A., Rassias, M.
- On the
Hierarchical Behavior of Solutions of the Maryland Equation in the
Semiclassical Approximation.
In collaboration with
A. Fedotov.
Mat. Zametki 108 (2020), no. 6, 941--946.
- The
complex WKB method for difference equations and Airy
functions.
In collaboration with
A. Fedotov.
SIAM J. Math. Anal. 51 (2019), no. 6, 4413--4447.
-
Semiclassical resolvent estimates for bounded
potentials.
In collaboration with M. Vogel.
Pure
and Applied Analysis Pure Appl. Anal. 1 (2019), no. 1,
1--25.
-
Difference equations, uniform quasiclassical asymptotics and Airy
functions.
In collaboration with A. Fedotov.
2018 Days on Diffraction (DD), St. Petersburg,
2018,
- Complex WKB
method for difference equations with meromorphic
coefficients.
In collaboration with A. Fedotov.
2017 Days on Diffraction (DD), St. Petersburg, 2017, pp. 110-112.
doi : 10.1109/DD.2017.8168006
-
Stark-Wannier ladders and cubic exponential sums.
In
collaboration with A. Fedotov.
no. 3, 81--85 Funct. Anal. Appl.
50 (2016).
- Resonances for
large one-dimensional ``ergodic'' systems
Anal. PDE 9 (2016), no. 2, 259--352.
- Optimal
Wegner estimate and the density of states for N-body, interacting
Schrödinger operators with random potentials
In
collaboration with P. Hislop.
Markov Process. Related Fields 21
(2015), no. 3, part 1, 519--536.
- Spectral
statistics for random Schrödinger operators in the localized
regime
In collaboration with F. Germinet.
Jour. Eur. Math. Soc. 16 (2014), vol. 9, 1967--2031
- Électrons en interaction dans un milieu aléatoire
Gazette des Mathématiciens, no 142, Octobre 2014.
- Enhanced Wegner
and Minami estimates and eigenvalue statistics of random Anderson
models at spectral edges
In collaboration with
F. Germinet.
Ann. Henri Poincaré 14 (2013), vol. 5,
1263--1285.
- Inverse tunneling
estimates and applications to the study of spectral statistics of
random operators on the real line
J. Reine
Angew. Math. 690 (2014), 79--113.
- Global
Poissonian behavior of the eigenvalues and localization centers of
random operators in the localized phase.
Séminaire "Équations aux Dérivées
Partielles" de l'Ecole Polytechnique (2010-2011),
- Asymptotic
ergodicity of the eigenvalues of random operators in the localized
phase
Probab. Theory Related Fields 155 (2013),
vol. 3--4, 867--909.
- Resonances for
"large" ergodic systems in one dimension: a review
In "Spectral Analysis of Quantum
Hamiltonians": proceedings of the conference "Spectral Days 2010"
Editors: R. Benguria, E. Friedman, M. Mantoiu editors.
Operator Theory Advance and applications, vol. 224, pp 171--182
(2012). Birkhäuser .
- Understanding the Random
Displacement Model: From Ground-State Properties to
Localization
In collaboration with M. Loss,
S. Nakamura, G. Stolz.
In "Spectral Analysis of Quantum
Hamiltonians": proceedings of the conference "Spectral Days 2010"
Editors: R. Benguria, E. Friedman, M. Mantoiu editors.
Operator Theory Advance and applications, vol. 224, pp 183--220
(2012). Birkhäuser .
- An exact
renormalization formula for Gaussian exponential sums and
applications.
In collaboration with A. Fedotov.
Amer. Jour. Math. Vol. 143 n° 3, pp. 711-748 (2012)
- Localization for
the random displacement model
In collaboration with
M. Loss, S. Nakamura, G. Stolz.
Duke Math. Jour. Vol. 161
(2012), n° 4, pp. 587-621.
- The
Gross-Pitaevskii functional with a random background potential and
condensation in the single particle ground state.
In
collaboration with B. Metzger.
Math. Phys. Anal. Geom. 14
(2011), n° 4, pp. 321-341.
- Spectral statistics for the
discrete Anderson model in the localized regime
In
collaboration with F. Germinet.
Proceedings of the conference
« Spectra of Random Operators and Related Topics »,
Université de Kyoto, Kyoto, Japon, 2 - 4 décembre
2009. Eds: N. Minami, N. Ueki.
RIMS Kôkyûroku
Bessatsu, B27, pp. 11-24, Res. Inst. Math. Sci. (RIMS), Kyoto,
2011.
- Decorrelation
estimates for the eigenlevels of the discrete Anderson model in the
localized regime.
Comm. Math. Phys. Vol. 303,
pp. 233-260 (2011).
- Lifshitz
tails for alloy type models in a constant magnetic
field
J. Phys. A: Math. Theor. 43 (2010)
474029. Volume dedicated to the memory of Pierre Duclos.
- Lifshitz tails for
generalized alloy type random Schrödinger
operators.
In collaboration with S. Nakamura.
Analysis and PDE, vol 3, pp. 409-426 (2010).
- Localization for the random displacement
model at weak disorder.
In collaboration with
F. Ghribi.
Annales Henri Poincaré, Vol. 11, Issue 1,
pp. 127-149 (2010).
- Absolute continuity of the spectrum of a
Landau Hamiltonian perturbed by a generic periodic
potential.
Math. Annalen, Volume 347, Number 3, pp.
675-687 (2010).
- Lifshitz tails for alloy type random models in
constant magnetic fields: a short review.
Proceedings of
the Conference Spectral and Scattering Theory for Quantum Magnetic
Systems
CIRM, Marseille, France, July 7 - 11, 2008.
Eds:
P. Briet, F. Germinet, G. Raikov.
Contemporary Mathematics, vol.
500, pp. 153-158 (2009).
- The Fate of the Landau Levels under
Perturbations of Constant Sign
In collaboration with
G. Raikov.
Int. Math. Res. Not. IMRN 2009, n° 24,
4726--4734.
- The integrated density of states for an
interacting multiparticle homogeneous model and applications to the
Anderson model
In collaboration with H. Zenk.
Advances in Mathematical Physics. Vol. 2009, Article ID 679827, 15
pages, 2009.
- Localization on quantum graphs with random
edge lengths
In collaboration with
K. Pankrashkin.
Letters in Mathematical Physics, Volume 87, pp
99--114 (2009)
- Spectral
extrema and Lifshitz tails for non monotonous alloy type
models.
In collaboration with S. Nakamura.
Comm. Math. Phys. Volume 287, Issue3 (2009), Page 1133
- Pointwise existence of the Lyapunov exponent
for a quasi-periodic equation.
In collaboration with
A. Fedotov.
``Mathematical Results in Quantum Mechanics'':
Proceedings of the Qmath10 Conference, 10-15 September 2007
Editors: Ingrid Beltita, Gheorghe Nenciu, Radu Purice
World
Scientific, 2008
- Appendix to ``An invitation to random
Schrödinger operators'' by W. Kirsch
"Random
Schrödinger Operators", Panoramas et Synthèses, nb 25,
Soc. Math. France (2008).
- Lifshitz tails for some non monotonous random
models.
In collaboration with S. Nakamura.
Proceedings of the Séminaire "Équations aux Dérivées Partielles" de
l'École Polytechnique. (2007-2008). Talk
14.
- Localization on quantum graphs with random
vertex couplings
In collaboration with K. Pankrashkin
Jour. Stat. Phys. vol 131, pp 651--673 (2008).
- Localization for Schrödinger operators with
random vector potentials
In collaboration with F. Ghribi and P. D. Hislop.
Contemporary Mathematics, vol. 447, ``Adventures in mathematical
physics'',
Proceedings of the internationl conference in honor of
Jean-Michel Combes, Sept. 4-6, 2006, Eds Germinet, Hislop,
pp. 123-138.
- An optimal Wegner estimate and its application
to the global continuity of the integrated density of states for
random Schrödinger operators
In collaboration with JM. Combes and P. D. Hislop.
Duke
Math. Journal, vol 140, pp 469-498 (2007).
- Some new estimates on the spectral shift
function associated with random Schrödinger operators
In collaboration with JM. Combes and P. D. Hislop.
CRM Proceedings and Lecture Notes, vol. 42, "Probability and
Mathematical Physics",
Proceeding of the conference celebrating 65th
birthday of Stanislav Molchanov, Eds Dawson, Jaksic, Vainberg,
pp. 85-96.
- The width of
resonances for slowly varying perturbations of one-dimensional
periodic Schrödinger operators
In collaboration with M. Marx.
Exposé IV. Proceedings of
the Séminaire "Équations aux Dérivées Partielles" de l'École
Polytechnique (2005-2006), Exp. n° IV, 18 pp.
- Lifshitz Tails in
Constant Magnetic Fields.
In collaboration with G. Raikov.
Comm. Math. Phys. vol 267, pp 669-701 (2006).
- Strong resonant tunneling, level repulsion and
spectral type for one-dimensional adiabatic quasi-periodic
Schrödinger operators.
In collaboration with A. Fedotov.
Ann. Scient. ENS, vol
38, pp. 889-950 (2005).
A few videos showing the effects of level repulsion:
- &tau large
- &rho small
- &tau small et &rho large
- Continuity with respect to Disorder of the
Integrated Density of States.
In collaboration with P. Hislop et J. Schenker.
Ill. Math. Jour., vol 49, pp. 893-904 (2005).
- Weakly resonant tunneling interactions for
adiabatic quasi-periodic Schrödinger operators.
In collaboration with A. Fedotov.
Mémoires Soc. Math. France, vol 104 (2005).
- The band-edge behavior of the density of
surfacic states.
In collaboration with
W. Kirsch.
Mathematical Physics, Analysis and Geometry, vol 8, pp.
315 - 360 (2006).
- Renormalization of exponential sums and matrix
cocycles.
In collaboration with A. Fedotov.
Exposé
XVI. Proceedings of the Séminaire "Equations aux Dérivées
Partielles" de l'École Polytechnique (2004-2005).
A few
videos showing the graphs of the exponential sums (the
consecutive values of the sum are linearly interpolated):
- k=2 et
a=&pi/10 (~38 MB)
- k=3/2 et a=&pi/10 (~48 MB)
- k=8/5 et a=&pi/10 (~4 MB)
- k=3/2 et a=1 (~21 MB)
- Absolutely continuous spectrum for the
isotropic Maxwell operator with coefficients that are periodic in
some directions and decay in others.
In collaboration with N. Filonov.
Comm. Math. Phys.
vol. 258 , pp. 75--85, (2005).
-
On the absolutely continuous spectrum of one dimensional
quasi-periodic Schrödinger operators in the adiabatic limit.
In collaboration with A. Fedotov.
Transactions A.M.S.
vol. 357, pp. 4481-4516 (2005).
- Global Continuity of the Integrated Density
of States for Random Landau Hamiltonians
In collaboration with J.M. Combes, P. Hislop and
G. Raykov.
Comm. Partial Differential Equations, vol. 29, pp.
1187--1213 (2004).
-
Opérateurs de Schrödinger quasi-périodiques adiabatiques :
Interactions entre les bandes spectrales d'un opérateur périodique.
In collaboration with A. Fedotov.
Exposé VIII. Proceedings
of the Séminaire "Equations aux Dérivées Partielles" de l'École
Polytechnique (2003-2004).
- On the singular spectrum for adiabatic
quasi-periodic Schrödinger operators on the real line.
In collaboration with A. Fedotov.
Annales H. Poincaré,
vol. 5, pp. 929--978 (2004).
- Geometric tools of the adiabatic complex WKB
method.
In collaboration with A. Fedotov.
Asymptotic Analysis, vol. 39(3,4), pp. 309--357 (2004).
- Absolute continuity of the spectrum of a
Schrödinger operator with a potential which is periodic in some
directions and decays in others
In collaboration with
N. Filonov.
Documenta Mathematica, vol. 9, pp. 107--121
(2004). Erratum in the same volume.
-
A note on Anderson localization for the random hopping model.
In collaboration with S. Nakamura.
Jour. Math. Phys., vol
44, pp. 4975--4980 (2003)
- The spectral theory of adiabatic
quasi-periodic operators on the real line.
In collaboration with A. Fedotov.
Markov Processes and
Related Fields, vol. 9, pp. 579 -- 615 (2003).
-
Regularity properties for the density of states of random
Schrödinger operators.
In collaboration with J.M. Combes et P. Hislop.
Contemporary Mathematics, Vol. 339, pp. 15 -- 25 (2003).
- Anderson localization for 2D discrete Schrödinger operator with
random vector potential.
In collaboration with S. Nakamura, F. Nakano,
Y. Nomura.
Annales Henri Poincaré, vol. 4, pp. 795--811 (2003).
-
Local and Global Continuity of the Integrated Density of States
In collaboration with J.M. Combes and P. Hislop.
Contemp. Math., vol. 327, pp. 61--74 (2003).
-
Hölder continuity of the integrated density of states for
some random operators at all energies.
In collaboration with J.M. Combes and P. Hislop.
I.M.R.N., vol 2003 [4], pp. 179--209 (2003).
-
Lifshitz tails for 2-dimensional random Schrödinger
operators
In collaboration with T. Wolff.
Journal d'Analyse Mathématique, vol. 88, pp. 63--147 (2002)
-
Weak disorder localization and Lifshitz tails.
Comm. Math. Phys., vol. 232, pp 125-155 (2002).
- The Integrated Density Of States For Some
Random Operators With Nonsign Definite Potentials
In collaboration with P. Hislop.
Jour. Func. Anal., vol. 195, pp 12--47 (2002).
-
Weak disorder localization and Lifshitz tails : continuous
Hamiltonians.
Ann. I.H.P. vol. 3, pp 711--737 (2002).
- Une remarque à propos des asymptotiques de
Lifshitz internes.
C.R.A.S Série I vol. 335 pp
87--92 (2002).
-
Anderson transitions for a family of almost periodic Schrödinger
equations in the adiabatic case
In collaboration with A. Fedotov.
Commun. Math. Phys. vol. 227, pp. 1--92 (2002).
- Mathematical Analysis of the Photoelectric
Effect.
In collaboration with V. Bach et H. Zenk.
Advances in Theoretical and Mathematical Physics vol 5, pp 969--999
(2002).
- Internal Lifshitz tails for Schrödinger
operators with random potentials
Jour. Math. Phys. vol. 43 pp 2948--2958 (2002)
- Asymptotiques de Lifshitz.
Exposé IV. Proceedings of the Séminaire "Equations aux
Dérivées Partielles", École Polytechnique (2001-2002).
-
Internal Lifshitz tails for random Schrödinger operators
In collaboration with T. Wolff.
Proceedings of the I.C.M.P. 2000, Imperial
College, London.
Eds A. Fokas, A. Grigoryan, T. Kibble,
B. Zegarlinski.
International Press, 2002
- The Wegner estimate and the integrated density of states
for some random operators
In collaboration with J.-M. Combes, P. D. Hislop and S.
Nakamura.
Proceedings of the ``Spectral and Inverse
Spectral theories of Schrödinger Operators'', 14-20/12/2000, Goa
(Inde).
Proceedings of the Indian Academy of Sciences,
Mathematical Sciences, vol. 112 (1), pp. 31-55 (2002).
- Lifshitz tails for random perturbations of
periodic Schrödinger operators
Proceedings of the ``Spectral and Inverse Spectral theories
of Schrödinger Operators'', 14-20/12/2000, Goa (Inde).
Proceedings of the Indian Academy of Sciences, Mathematical
Sciences, vol. 112 (1), pp. 147-163 (2002).
- A complex WKB method for adiabatic
problems
In collaboration with A. Fedotov.
Asymptotic
Analysis, vol. 27 pp. 219--264 (2001).
- Endpoints of the spectrum of periodic
operators are generically simple
In collaboration with J. Ralston.
Meth. Appl. Anal., volume 7 dedicated to C. Morawetz, pp 459-464
(2000).
- Precise high energy asymptotics for the
integrated density of states of an unbounded random Jacobi matrix.
Rev. Math. Phys. vol. 12 [4], pp 575-620 (2000).
- Lifshitz tails for random Schrödinger
operators with negative singular Poisson potential.
In collaboration with L. Pastur.
Comm. Math. Phys. vol. 206, pp 57-103 (1999).
- Internal Lifshits tails for random
perturbations of periodic Schrödinger operators.
Duke Math. Jour. vol 98, pp 335-396
(1999).
- Transitions d'Anderson pour des opérateurs de
Schrödinger quasi-périodiques en dimension 1.
In collaboration with A. Fedotov.
Exposé
IV. Proceedings of the Séminaire "Equations aux Dérivées Partielles",
École Polytechnique (1998-1999).
- Coexistence of different spectral types for
almost periodic Schrödinger equations in dimension one.
In collaboration with A. Fedotov.
Proceedings
of the conference ``Mathematical Results in Quantum Mechanics
(QMath7)'', Prague, 22-26 June 1998 Operator Theory: Advances and
Applications, vol 108, pp 243-251.
- A short introduction to the theory of random
Schrödinger operators.
Viet. Jour. Math. Vol. 26 [3] (1998).
- Band edge behaviour for the integrated density
of states of random Jacobi matrices in dimension 1.
Jour. Stat. Phys., vol. 90 [3-4], pp. 927-947
(1998).
- Etude semi-classique d'une perturbation d'un opérateur
de Schrödinger périodique : cas d'un nombre fini de perturbations.
Asymp. Anal., vol. 15, pp 55-102 (1997).
- On the spectrum of odd order self-adjoint
ordinary differential operators on the real line with quasi-periodic
coefficients.
In collaboration with B. Grébert et J.-C. Guillot.
Jour. Diff. Equ., vol. 135, pp. 41-65 (1997).
- Generic simplicity for resonances.
In collaboration with M. Zworski.
Helv. Phys. Act.,
vol 68, pp. 531-538 (1995).
- Développement asymptotique pour lqa densité
d'états d'un opérateur de Schrödinger aléatoire.
Exposé IV. Proceedings of the Séminaire "Équations aux
Dérivées Partielles", École Polytechnique (1995-1996).
- An asymptotic expansion for the density of
states of a random Schrödinger operator with Poisson disorder.
Jour. Funct. Anal., vol 145, pp. 267-295 (1997).
- Valeurs propres et résonances au voisinage
d'un seuil.
In collaboration with A. Grigis.
Bull. S.M.F. , vol
124, pp 477-501 (1996).
- The density of states for multidimensional
continuous random Schrödinger operators with singular randomness.
Actes de la conférence ``Spectral Theory of Schrödinger
operators'', Madras (Inde) Décembre 1995. The paper
is here.
- A low concentration asymptotic expansion for
the density of states of a random Schrödinger operator with Bernoulli
disorder.
Rand. Op. Stoch. Eq., vol 3, pp. 315-332 (1995).
- Resonances for perturbations of a
semi-classical periodic Schrödinger operator.
Ark. Mat., vol. 32, pp 323-371 (1994).
- Localization for some continuous random
Schrödinger operators.
Comm. Math. Phys., vol. 167, pp. 553-571 (1995).
- Localization for continuous random Schrödinger
operators in the semiclassical limit.
Proceedings
of the conference ``Asymptotic Methods in Spectral Theory'', Institut
Euler (Saint Pétersbourg), September 1993,
St Petersburg
Math. Journal, vol. 8, pages 105--110 (1997)
- Localization for semi-classical continuous
random Schrödinger operators II: the random displacement
model.
Helv. Phys. Act., vol. 66, pp. 810-841
(1993).
- Localisation pour des opérateurs de
Schrödinger aléatoires dans $L^2(R^d)$ : un modèle
semi-classique.
Ann. Institut Fourier., vol 45, pp. 265-316
(1995).
- Etude semi-classique d'une perturbation d'un
opérateur de Schrödinger périodique.
Ann. Inst. Henri
Poincaré, sér. Phys. Théor., Vol 55, pages 459--509 (1991).
- Impuretés dans une structure
périodique.
Exposé no 20, Actes des Journées E.D.P, St
Jean-de-Monts, 1990.
Unpublished: