GTA Seminar - Wednesday, 10 September, 11:00-12:00 in Carlaw 535A
Please join us for lunch after the talk!
James Parkinson (Sydney)
Abstract
The celebrated Multiplicative Ergodic Theorem of Oseledets shows
that under a finite first moment assumption, the product of random real iid
matrices behaves asymptotically like the sequence of powers of some fixed
positive definite symmetric matrix. In 1989 Vadim Kaimanovich showed that
this property can be expressed in purely geometric terms using the symmetric
space associated to
In this talk we will discuss a p-adic analogue of this story. In this setting the symmetric space is replaced by the affine building of the p-adic group. We define regular sequences in affine buildings, and give a characterisation of these sequences in terms of analogues of the spherical and horospherical coordinates from the real theory. We then discuss applications to a Multiplicative Ergodic Theorem for Lie groups defined over p-adic fields. This is joint with W. Woess.