Event Detail

Event Type: 
Probability Seminar
Tuesday, January 21, 2014 - 07:00
Furman Hall 105

Speaker Info

University of Sao Paulo

For a single nonnegative dxd matrix, there are these three classical results: the Perron-Frobenius Theorem (a primitive matrix has a unique nonnegative eigenvector), the Frobenius decomposition theorem (the elements 1,2,...,d can be grouped into communicating states, equivalently the matrix has an upper triangular block form, with primitive or zero blocks on the diagonal after taking some power) and the Frobenius-Victory theorem (which identifies eigenvectors of such an upper triangular matrix in terms of the primitive blocks and "distinguished eigenvalues".) 

In this talk we describe nonstationary versions of these theorems, which are key tools in a study of the ergodic theory of adic transformation.s (Joint with Marina Talet of Aix-Marseille University).