A Note on Matrix Multiplicative Cascades and Bindweeds

#### M.V. Menshikov, D. Petritis, S.Yu. Popov

2005, v.11, Issue 1, 37-54

ABSTRACT

We study the problem of Mandelbrot's multiplicative cascades, but with random matrices instead of random variables. Then, we introduce a new model (which we call the bindweed model), which can be viewed as a random string in a random environment on a tree, and show that the classification of this model from the point of view of positive recurrence can be obtained from the corresponding classification of the matrix-valued multiplicative cascades.

Keywords: Markov chain,trees,random environment,recurrence criteria,matrix multiplicative cascades