On the spectral norm of Gaussian random matrices

TL;DRAbstract

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d times d"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo> × </mml:mo> <mml:mi>d</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">d\times d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> symmetric random matrix with independent but nonidentically distributed Gaussian entries. It has been conjectured by Latała that the spectral norm of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics>

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