Michael Aizenman        

Professor of Physics and Mathematics
Jadwin Hall, Princeton University
Princeton NJ, 08544
Tel: (609) 258-4380

aizenman at princeton dot edu

Typically, many of the interesting phenomena encountered in statistical mechanics are beyond the reach of exact solutions and perturbative methods. Our goal has been to develop rigorous methods which can shed light on the critical behavior even in such situations. A recurring theme has been the appearance of stochastic geometric effects which play important roles in the behavior of critical system. The work has contributed to the nascence of the current field of random fractal structures which capture the scaling limits of many critical two dimensional systems, and which bear close relations with conformal field theories. Our previous works have rigorously established the existence of model-dependent upper critical dimensions, above which the critical behavior simplifies.

Works on quantum spectra and dynamics have provided new methods for dealing with localization caused by disorder, and conversely for establishing the persistence of extended states in the presence of disorder. On the latter topic the success has been rather limited; the issues continues to provide a mathematical challenge. Other goals of current work include shedding light on spectral gaps for systems with disorder, and conjectured relations with the distributions known from random matrix models.

Current editorial service: Comm. Math. Phys., Analysis and PDE, Rev. Math. Phys..