Exact dimension of Furstenberg measures
Francois Ledrappier (LPSM (UMR\_8001)), Pablo Lessa (IMERL)

TL;DR
This paper establishes the exact dimensionality of Furstenberg measures on flag spaces for certain discrete probability measures on SL d(R), under specific integrability and non-degeneracy conditions.
Contribution
It provides a precise dimension formula for Furstenberg measures in the discrete case, extending previous results to a broader class of measures.
Findings
Furstenberg measures are exact-dimensional under given conditions
Dimension formula derived for discrete measures on SL d(R)
Results apply under integrability and non-degeneracy assumptions
Abstract
For a probability measure on SL d (R), we consider the Furstenberg stationary measure on the space of flags. Under general non-degeneracy conditions, if is discrete and if g log g d(g) < +, then the measure is exact-dimensional.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Stochastic processes and statistical mechanics
