grandes-ecoles 2018 QV.2

grandes-ecoles · France · x-ens-maths__pc Not Maths Probability Inequality and Tail Bound Proof
We fix $A \in \mathcal{M}_{n}(\{-1,1\})$ and denote $$m(A) := \min(S(A) \cap \mathbb{N}).$$
By drawing inspiration from the previous question and the methods developed in Parts II and III, show that we also have $$m(A) \leqslant \sqrt{2n \ln(2n)}.$$ 
We fix $A \in \mathcal{M}_{n}(\{-1,1\})$ and denote
$$m(A) := \min(S(A) \cap \mathbb{N}).$$

By drawing inspiration from the previous question and the methods developed in Parts II and III, show that we also have
$$m(A) \leqslant \sqrt{2n \ln(2n)}.$$
Paper Questions
QI.1 QI.2 QI.3 QI.4 QI.5 QI.6 QII.1 QII.2 QII.3 QII.4 QII.5 QII.6 QIII.1 QIII.2 QIII.3 QIII.4 QIV.1 QIV.2 QIV.3 QIV.4 QV.1 QV.2