Applied Maths Seminar: Peneau -- Products of random matrices without moment conditions

Axel Peneau (University of Tours) is visiting on Monday and Tuesday next week, and will
be giving a seminar on "Products of random matrices without moment conditions".  

This will take place on Tuesday 13 May at 2pm in the SMRI Seminar Room (Macleay
301)--note unusual everything.

Title: Products of random matrices without moment conditions 

Abstract: We consider a product of random Matrices M_n = X_0 ...  X_{n-1}.  The (X_i)
are i.i.d.  and generate a Zariski dense semi-group.  We are interested in the limit
behaviour of M_n.  I will first give a quick overview of historical results, whose
proofs rely on moment assumptions for the logarithm of the norm.  Then I will state some
of my results obtained using the pivoting technique, putting emphasis on the optimality
of moment assumptions.  Most notably, the law of large numbers for the spectral radius
and the coefficients hold with a first moment assumption only and a contraction result
equivalent to the simplicity of the Lyapunov spectrum holds without moment assumptions.
If time permits, I will give an idea of the proof of these results.