Laszlo Erdos - Major Publications#

[1] L. Erdos, A. Knowles: The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Commun. Math. Phys. 333 no. 3, 1365-1416 (2015)

[2] P. Bourgade, L. Erdos, H.-T. Yau: Edge universality of beta ensembles. Commun. Math. Phys. 332 no. 1, 261-354 (2014)

[3] P. Bourgade, L. Erdos, H.-T. Yau: Universality of General beta Ensembles.
Duke Math. J. 163 , no. 6, 1127-1190, (2014)

[4] L. Erdos, S. Fournais, J.P. Solovej: Scott correction for large atoms and molecules in a self-generated magnetic field. Comm. Math. Phys. 312 no. 3 (2012), 847-882.

[5] L. Erdos, D. Hasler, Wegner estimate and Anderson localization for random magnetic felds. Commun. Math. Phys. 309, No. 2, 507-542 (2012)

[6] L. Erdos, H.-T. Yau, J. Yin, Rigidity of Eigenvalues of Generalized Wigner Matrices. Adv. Math. 229, no. 3, 1435-1515 (2012)

[7] L. Erdos, B. Schlein , H.-T. Yau, Universality of Random Matrices and Local Relaxation Flow. Invent. Math. 185 (2011), no.1, 75-119.

[8] L. Erdos, B. Schlein, H.-T. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein Condensate. Ann. Math. (2) 172, no.1, 291--370 (2010)

[9] L. Erdos, M. Salmhofer, H.-T. Yau, Quantum diffusion of the random Schrodinger evolution in the scaling limit. Acta Math. 200, no.2, 211-277 (2008)

[10] L. Erdos, B. Schlein, H.-T. Yau, Derivation of the Cubic Non-linear Schrodinger Equation from Quantum Dynamics of Many-Body Systems. Invent. Math. 167, 515-614 (2007)

Justification of choice:

[1] Provides the rigorous verification of the celebrated Altshuler-Shklovskii formula in physics for the mesoscopic spectral statistics of energy levels of a disordered quantum system

[2][3] Prove the Wigner-Dyson-Mehta universality for general beta ensembles in the entire spectrum

[4] Introduces the concept of self-generated magnetic field in the rigorous theory of ground state energy of large atoms and molecules in the limit of large nuclear charge and proves a two term asymptotics. The Scott correction is new and it shows that magnetic effects are more substantial than previously thought.

[5] First proof of Anderson localization with a random magnetic field with nonzero flux. Ingeniously resolves the main challenge of lack spectral monotonicity.

[6][7] Solve the half centrury old Wigner-Dyson-Mehta universality conjecture for Wigner matrices. The solution reveals the genuine origin of the universal spectral behavior of large random matrices: universality is a consequence of the decay to equilibrium of an interacting stochastic particle system. (Freeman Dyson noticed this connection in 1962 and he challenged the mathematics community that "a rigorous proof that this picture is accurate would require a much deeper mathematical analysis".)

[8][10] Derive the Gross-Pitaevskii equation starting from first principle quantum dynamics with a singular repulsive potential. Puts the dynamical mean field theory of the Bose Einstein condensation on solid mathematical ground.

[9] First rigorous derivation of quantum diffusion of a single quantum particle in an uncorrelated random potential.