Series:
Combinatorics Seminar
Friday, February 23, 2018 - 15:05
1 hour (actually 50 minutes)
Location:
Skiles 005
Organizer:
I will describe two new local limit theorems on the
Heisenberg group, and on an arbitrary connected, simply connected
nilpotent Lie group. The limit theorems admit general driving measures
and permit testing against test functions with an arbitrary
translation on the left and the right. The techniques introduced include
a rearrangement group action, the Gowers-Cauchy-Schwarz inequality, and
a Lindeberg replacement scheme which approximates the driving measure
with the corresponding heat kernel. These
results generalize earlier local limit theorems of Alexopoulos and
Breuillard, answering several open questions. The work on the
Heisenberg group is joint with Persi Diaconis.