Lower bound for Expected Value of Euclidean Norm

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If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
$$
mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
$$
I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.



Thank you in advance.







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    up vote
    0
    down vote

    favorite












    If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
    $$
    mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
    $$
    I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.



    Thank you in advance.







    share|cite|improve this question






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
      $$
      mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
      $$
      I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.



      Thank you in advance.







      share|cite|improve this question












      If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
      $$
      mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
      $$
      I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.



      Thank you in advance.









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 17 at 2:54









      M.Shen

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