Semigroups for One-Dimensional Schrödinger Operators with Multiplicative White Noise.

In this talk, we are interested in understanding the semigroups generated by a class of Schrödinger operators whose potential is perturbed by a multiplicative Gaussian white noise. In the first part of the talk, we will discuss applications in random matrix theory and mathematical physics that motivate our investigations. Then, we will discuss some of the technical challenges involved with our program and show how these problems can be overcome in one dimension.