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, meaning that \(p\in {\mathsf {s}}\) , then \(\delta n_{k}(p,0)\equiv \delta n_{k}(p)\) is a martingale difference sequence. furthermore, for all \(k\ge 1\) , $$\begin{aligned} {\mathbb {e}}[\delta m_{k}\vert {\mathcal {f}}_{k}]\le \frac{5\rho _{k}...
In fact, the Boltzmann case 𝑞=0q=0, describing the statistics of classical particles concerning the physical meaning, is also known as free because it naturally arises from a particular case of quantum probability called free probability (see, e.g., [3]). In the setting of quantum ...