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October 16, 2025Open Access

Singularity of Furstenberg measure for infinite covolume discrete subroups in higher rank

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The associated hitting measure on the Furstenberg boundary is singular when subgroups have infinite covolume.
This finding contrasts with previous work on Brownian motion discretization and holds true for higher rank groups.
The study focuses on discrete, Zariski-dense subgroups of semisimple lie groups that exhibit Property (T).
This research contributes to understanding random walks on groups and their implications on hitting measures.

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This analysis shows hitting measures can be singular for symmetric random walks in discrete subgroups, indicating a departure from earlier results.

Lee et al. (2025) studied this question.

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This analysis shows hitting measures can be singular for symmetric random walks in discrete subgroups, indicating a departure from earlier results.