For every finite real self-similar probability measure with positive weights and nonzero contraction ratios of absolute value below one, dim_H μ=min(1,h_RW/χ), even with exact overlaps and unequal signed ratios.
For every finite real self-similar probability measure with positive weights and nonzero contraction ratios of absolute value below one, dim_H μ=min(1,h_RW/χ), even with exact overlaps and unequal signed ratios.
For every finite real self-similar probability measure with positive weights and nonzero contraction ratios of absolute value below one, dim_H μ=min(1,h_RW/χ), even with exact overlaps and unequal signed ratios.
If correct, resolves the entropy-rate dimension conjecture for finite real self-similar measures.
Does random-walk entropy rate determine the dimension of real self-similar measures with exact overlaps?
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OpenAI reports the entropy-rate dimension formula for self-similar measures
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