Anderson Localization in dimension two for singular noise, part two

Mathematical Physics and Analysis Working Seminar
Friday, March 3, 2023 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 006
Omar Hurtado – UC Irvine
Burak Hatinoglu

We will continue our discussion of the key ingredients of a multi-scale analysis, namely resolvent decay and the Wegner type estimate. After briefly discussing how the Wegner estimate is obtained in the regime of regular noise, we will discuss the strategy used in Bourgain-Kenig (2005) and Ding-Smart (2018) to obtain analogues thereof using some form of unique continuation principle.

From here, we'll examine the quantitative unique continuation principle used by Bourgain-Kenig, and the lack of any even qualitative analogue on the two-dimensional lattice. From here, we'll discuss the quantitative probabilistic unique continuation result used in Ding-Smart.