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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Trouble understanding a Lemma in Pastur's Paper

I'm having trouble understand Eq 3.51 Lemma 3.3 in https://arxiv.org/pdf/2001.06188.pdf The basic premise is $$\begin{align} &\eta _{j}(t)=t^{1/2}\eta _{j}+(1-t)^{1/2}q_{n}^{1/2}\gamma _{j}, \;t \in [ …
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