Event time:

Monday, September 9, 2019 - 4:15pm

Location:

LOM206

Speaker:

Jialun Li

Speaker affiliation:

University of Zürich

Event description:

Let mu be a Borel probability measure on SL(2,R) with a finite

exponential moment, such that the support of mu generates a Zariski

dense subgroup in SL(2,R). We can define a unique probability measure on

the circle, which is called the mu stationary measure or Furstenberg

measure. We will prove, using Bourgain’s discretized sum-product

estimate, that the Fourier coefficients of this measure go to zero with

a polynomial speed. Starting from this result, we can obtain a spectral

gap of the transfer operator, whose properties enable us to get an

exponential error term in the renewal theorem in the context of random

products of matrices.