Measure Rigidity and Equidistribution for Fractal Carpets

Q: What does this research mean for the field?

Pushforward measures of a Bernoulli measure stationary for a random walk generated by contracting rational affine dilations equidistribute along any diverging sequence of diagonal matrices that expand the first d dimensions. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Osama Khalil; Manuel Luethi; Barak Weiss

doi:10.1007/s00039-026-00749-x

September 10, 2026Geometric and Functional AnalysisOpen Access

Measure Rigidity and Equidistribution for Fractal Carpets

View Full Paper

Ask AI

Bookmark

Share

Key Points

Investigate measure rigidity and establish the equidistribution of pushforward measures generated by stationary fractal measures on homogeneous lattice spaces.
Constructed stationary Bernoulli measures supported on fractal attractors generated by contracting rational affine dilations, such as Sierpiński carpets and Menger sponges.
Mapped attractor points to unimodular lattices in SL_{d+1}(R)/SL_{d+1}(Z) via an explicit lattice embedding.
Analyzed the asymptotic distribution of pushforward measures under diverging sequences of diagonal expansion matrices.
Proved the equidistribution of pushforward measures along diverging sequences of diagonal matrices expanding the first d coordinates.
Established measure rigidity properties for high-dimensional fractal measures embedded into homogeneous spaces.

No abstract yet

We only have this paper's title and publication details.

Read it at the source

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Mathematical analysis demonstrates equidistribution of pushforward measures on lattice spaces for fractal attractors, indicating deep connections between dynamics and fractal geometry.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Khalil et al. (2026) studied this question.

synapsesocial.com/papers/6aa51e69327956e4761f84e1 https://doi.org/10.1007/s00039-026-00749-x

View Full Paper

Ask AI

Bookmark

Share

Measure Rigidity and Equidistribution for Fractal Carpets

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Measure Rigidity and Equidistribution for Fractal Carpets

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Keep reading

Keep reading