3 papers
math.DS2026
Weaker quantization dimension results for self-similar measures
Saurabh Verma, Shivam Dubey
In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some leve…
math.DS2025
Some results on Lower Assouad and quantization dimensions
Saurabh Verma, Ekta Agrawal, Shivam Dubey
In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( γ\in [0,1] \) is dense in \( Π(\mathbb{R}) \), the space of compact su…
math.DS2025
Quantization for a condensation system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , represents the rate at which the th quantization error of order …