I will discuss a problem of energy-driven pattern formation, in which the appearance of two distinct phases caused by short-range attractive forces is frustrated by a long-range repulsive force. I will focus on the regime of strong compositional asymmetry, in which one of the phases has very small volume fraction, thus creating small "droplets" ...
Creator:
Muratov, Cyrill (New Jersey Institute of Technology)
Created:
2012-06-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I give an introduction to quantum diffusion and localization properties of eigenvectors of random band matrices. I give a short overview of the Anderson model, followed by a more in-depth discussion of random band matrices. After a survey of recent results, I sketch the main ideas of the proofs. I focus on two approaches: perturbative renormaliz...
Creator:
Knowles, Antti (Harvard University)
Created:
2012-06-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
(joint work with A. Guionnet). By solving a free analog of the Monge-Amp`ere equation, we prove a non-commutative analog of Brenier's monotone transport theorem: if an $n$-tuple of self-adjoint non-commutative random variables $Z_{1},...,Z_{n}$ satisfies a regularity condition (its conjugate variables $xi_{1},...,xi_{n}$ should be analytic in $Z...
Creator:
Shlyakhtenko, Dimitri (University of California, Los Angeles)
Created:
2012-06-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
