For stationary measures on the flags of R^d, the conditional measures along each one-dimensional flag foliation are exact dimensional with dimension equal to an entropy divided by the Lyapunov gap.
On the speed of distance stationary sequences
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d.\ matrix products, but our result has applications in various different contexts. In many situations it gives a method to estimate the speed, and in others it allows to obtain results of dimension drop for escape measures related to random walks. We show applications to stationary reversible random trees with conductances, Bernoulli bond percolation of Cayley graphs, and random walks on cocompact Fuchsian groups.
fields
math.DS 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Entropy and dimension of disintegrations of stationary measures
For stationary measures on the flags of R^d, the conditional measures along each one-dimensional flag foliation are exact dimensional with dimension equal to an entropy divided by the Lyapunov gap.