Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices
Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices
Abstract We evaluate, in the large- N limit, the complete probability distribution <?CDATA $\mathcal{P}(A,m)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">P</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> of the values A of the sum <?CDATA $\sum_{i = 1}^{N} |\lambda_i|^m$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:munderover> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> …